N1.qti

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<questestinterop xmlns="http://www.imsglobal.org/xsd/ims_qtiasiv1p2" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.imsglobal.org/xsd/ims_qtiasiv1p2 http://www.imsglobal.org/xsd/ims_qtiasiv1p2p1.xsd">
  <objectbank ident="N1">
    <qtimetadata>
      <qtimetadatafield><fieldlabel>bank_title</fieldlabel><fieldentry>Differential Equations -- N1</fieldentry></qtimetadatafield>
    </qtimetadata>
  <item ident="N1-2568" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 2568"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-{\left(t + 4\right)} {\left(t - 1\right)} {y'} - e^{\left(3 \, t\right)} = {\left(t - 6\right)} {y} e^{t} \hspace{2em} x( -3 )= -8" alt="-{\left(t + 4\right)} {\left(t - 1\right)} {y'} - e^{\left(3 \, t\right)} = {\left(t - 6\right)} {y} e^{t} \hspace{2em} x( -3 )= -8" title="-{\left(t + 4\right)} {\left(t - 1\right)} {y'} - e^{\left(3 \, t\right)} = {\left(t - 6\right)} {y} e^{t} \hspace{2em} x( -3 )= -8" data-latex="-{\left(t + 4\right)} {\left(t - 1\right)} {y'} - e^{\left(3 \, t\right)} = {\left(t - 6\right)} {y} e^{t} \hspace{2em} x( -3 )= -8"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-%7B%5Cleft(t%20+%204%5Cright)%7D%20%7B%5Cleft(t%20-%201%5Cright)%7D%20%7By'%7D%20-%20e%5E%7B%5Cleft(3%20%5C,%20t%5Cright)%7D%20=%20%7B%5Cleft(t%20-%206%5Cright)%7D%20%7By%7D%20e%5E%7Bt%7D%20%5Chspace%7B2em%7D%20x(%20-3%20)=%20-8" alt="-{\left(t + 4\right)} {\left(t - 1\right)} {y'} - e^{\left(3 \, t\right)} = {\left(t - 6\right)} {y} e^{t} \hspace{2em} x( -3 )= -8" title="-{\left(t + 4\right)} {\left(t - 1\right)} {y'} - e^{\left(3 \, t\right)} = {\left(t - 6\right)} {y} e^{t} \hspace{2em} x( -3 )= -8" data-latex="-{\left(t + 4\right)} {\left(t - 1\right)} {y'} - e^{\left(3 \, t\right)} = {\left(t - 6\right)} {y} e^{t} \hspace{2em} x( -3 )= -8"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-4,1)" alt="(-4,1)" title="(-4,1)" data-latex="(-4,1)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-4,1)" alt="(-4,1)" title="(-4,1)" data-latex="(-4,1)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-3781" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 3781"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-{\left(t + 6\right)} {\left(t - 1\right)} {y} - {\left(t^{2} + 1\right)} {y'} = {\left(t - 6\right)} e^{t} \hspace{2em} x( 5 )= -1" alt="-{\left(t + 6\right)} {\left(t - 1\right)} {y} - {\left(t^{2} + 1\right)} {y'} = {\left(t - 6\right)} e^{t} \hspace{2em} x( 5 )= -1" title="-{\left(t + 6\right)} {\left(t - 1\right)} {y} - {\left(t^{2} + 1\right)} {y'} = {\left(t - 6\right)} e^{t} \hspace{2em} x( 5 )= -1" data-latex="-{\left(t + 6\right)} {\left(t - 1\right)} {y} - {\left(t^{2} + 1\right)} {y'} = {\left(t - 6\right)} e^{t} \hspace{2em} x( 5 )= -1"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-%7B%5Cleft(t%20+%206%5Cright)%7D%20%7B%5Cleft(t%20-%201%5Cright)%7D%20%7By%7D%20-%20%7B%5Cleft(t%5E%7B2%7D%20+%201%5Cright)%7D%20%7By'%7D%20=%20%7B%5Cleft(t%20-%206%5Cright)%7D%20e%5E%7Bt%7D%20%5Chspace%7B2em%7D%20x(%205%20)=%20-1" alt="-{\left(t + 6\right)} {\left(t - 1\right)} {y} - {\left(t^{2} + 1\right)} {y'} = {\left(t - 6\right)} e^{t} \hspace{2em} x( 5 )= -1" title="-{\left(t + 6\right)} {\left(t - 1\right)} {y} - {\left(t^{2} + 1\right)} {y'} = {\left(t - 6\right)} e^{t} \hspace{2em} x( 5 )= -1" data-latex="-{\left(t + 6\right)} {\left(t - 1\right)} {y} - {\left(t^{2} + 1\right)} {y'} = {\left(t - 6\right)} e^{t} \hspace{2em} x( 5 )= -1"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-\infty,+\infty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-%5Cinfty,+%5Cinfty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-6293" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 6293"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-{y'} e^{\left(3 \, t\right)} = {\left(t + 4\right)} {y} e^{t} + {\left(t + 1\right)} {\left(t - 6\right)} \hspace{2em} x( -1 )= -2" alt="-{y'} e^{\left(3 \, t\right)} = {\left(t + 4\right)} {y} e^{t} + {\left(t + 1\right)} {\left(t - 6\right)} \hspace{2em} x( -1 )= -2" title="-{y'} e^{\left(3 \, t\right)} = {\left(t + 4\right)} {y} e^{t} + {\left(t + 1\right)} {\left(t - 6\right)} \hspace{2em} x( -1 )= -2" data-latex="-{y'} e^{\left(3 \, t\right)} = {\left(t + 4\right)} {y} e^{t} + {\left(t + 1\right)} {\left(t - 6\right)} \hspace{2em} x( -1 )= -2"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-%7By'%7D%20e%5E%7B%5Cleft(3%20%5C,%20t%5Cright)%7D%20=%20%7B%5Cleft(t%20+%204%5Cright)%7D%20%7By%7D%20e%5E%7Bt%7D%20+%20%7B%5Cleft(t%20+%201%5Cright)%7D%20%7B%5Cleft(t%20-%206%5Cright)%7D%20%5Chspace%7B2em%7D%20x(%20-1%20)=%20-2" alt="-{y'} e^{\left(3 \, t\right)} = {\left(t + 4\right)} {y} e^{t} + {\left(t + 1\right)} {\left(t - 6\right)} \hspace{2em} x( -1 )= -2" title="-{y'} e^{\left(3 \, t\right)} = {\left(t + 4\right)} {y} e^{t} + {\left(t + 1\right)} {\left(t - 6\right)} \hspace{2em} x( -1 )= -2" data-latex="-{y'} e^{\left(3 \, t\right)} = {\left(t + 4\right)} {y} e^{t} + {\left(t + 1\right)} {\left(t - 6\right)} \hspace{2em} x( -1 )= -2"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-\infty,+\infty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-%5Cinfty,+%5Cinfty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-2706" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 2706"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-{y'} {\left(t + 4\right)} {\left(t - 6\right)} - t + 2 = {\left(t^{2} + 25\right)} {y} \hspace{2em} x( 0 )= 8" alt="-{y'} {\left(t + 4\right)} {\left(t - 6\right)} - t + 2 = {\left(t^{2} + 25\right)} {y} \hspace{2em} x( 0 )= 8" title="-{y'} {\left(t + 4\right)} {\left(t - 6\right)} - t + 2 = {\left(t^{2} + 25\right)} {y} \hspace{2em} x( 0 )= 8" data-latex="-{y'} {\left(t + 4\right)} {\left(t - 6\right)} - t + 2 = {\left(t^{2} + 25\right)} {y} \hspace{2em} x( 0 )= 8"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-%7By'%7D%20%7B%5Cleft(t%20+%204%5Cright)%7D%20%7B%5Cleft(t%20-%206%5Cright)%7D%20-%20t%20+%202%20=%20%7B%5Cleft(t%5E%7B2%7D%20+%2025%5Cright)%7D%20%7By%7D%20%5Chspace%7B2em%7D%20x(%200%20)=%208" alt="-{y'} {\left(t + 4\right)} {\left(t - 6\right)} - t + 2 = {\left(t^{2} + 25\right)} {y} \hspace{2em} x( 0 )= 8" title="-{y'} {\left(t + 4\right)} {\left(t - 6\right)} - t + 2 = {\left(t^{2} + 25\right)} {y} \hspace{2em} x( 0 )= 8" data-latex="-{y'} {\left(t + 4\right)} {\left(t - 6\right)} - t + 2 = {\left(t^{2} + 25\right)} {y} \hspace{2em} x( 0 )= 8"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-4,6)" alt="(-4,6)" title="(-4,6)" data-latex="(-4,6)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-4,6)" alt="(-4,6)" title="(-4,6)" data-latex="(-4,6)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-2976" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 2976"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y} {\left(t + 6\right)} {\left(t - 5\right)} + {y'} e^{\left(-2 \, t\right)} = -t \hspace{2em} x( -6 )= 2" alt="{y} {\left(t + 6\right)} {\left(t - 5\right)} + {y'} e^{\left(-2 \, t\right)} = -t \hspace{2em} x( -6 )= 2" title="{y} {\left(t + 6\right)} {\left(t - 5\right)} + {y'} e^{\left(-2 \, t\right)} = -t \hspace{2em} x( -6 )= 2" data-latex="{y} {\left(t + 6\right)} {\left(t - 5\right)} + {y'} e^{\left(-2 \, t\right)} = -t \hspace{2em} x( -6 )= 2"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%7By%7D%20%7B%5Cleft(t%20+%206%5Cright)%7D%20%7B%5Cleft(t%20-%205%5Cright)%7D%20+%20%7By'%7D%20e%5E%7B%5Cleft(-2%20%5C,%20t%5Cright)%7D%20=%20-t%20%5Chspace%7B2em%7D%20x(%20-6%20)=%202" alt="{y} {\left(t + 6\right)} {\left(t - 5\right)} + {y'} e^{\left(-2 \, t\right)} = -t \hspace{2em} x( -6 )= 2" title="{y} {\left(t + 6\right)} {\left(t - 5\right)} + {y'} e^{\left(-2 \, t\right)} = -t \hspace{2em} x( -6 )= 2" data-latex="{y} {\left(t + 6\right)} {\left(t - 5\right)} + {y'} e^{\left(-2 \, t\right)} = -t \hspace{2em} x( -6 )= 2"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-\infty,+\infty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-%5Cinfty,+%5Cinfty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-1378" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 1378"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{\left(t + 5\right)} {\left(t - 5\right)} {y} + t^{2} + 1 = -{\left(t + 2\right)} {y'} e^{t} \hspace{2em} x( 0 )= -5" alt="{\left(t + 5\right)} {\left(t - 5\right)} {y} + t^{2} + 1 = -{\left(t + 2\right)} {y'} e^{t} \hspace{2em} x( 0 )= -5" title="{\left(t + 5\right)} {\left(t - 5\right)} {y} + t^{2} + 1 = -{\left(t + 2\right)} {y'} e^{t} \hspace{2em} x( 0 )= -5" data-latex="{\left(t + 5\right)} {\left(t - 5\right)} {y} + t^{2} + 1 = -{\left(t + 2\right)} {y'} e^{t} \hspace{2em} x( 0 )= -5"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%7B%5Cleft(t%20+%205%5Cright)%7D%20%7B%5Cleft(t%20-%205%5Cright)%7D%20%7By%7D%20+%20t%5E%7B2%7D%20+%201%20=%20-%7B%5Cleft(t%20+%202%5Cright)%7D%20%7By'%7D%20e%5E%7Bt%7D%20%5Chspace%7B2em%7D%20x(%200%20)=%20-5" alt="{\left(t + 5\right)} {\left(t - 5\right)} {y} + t^{2} + 1 = -{\left(t + 2\right)} {y'} e^{t} \hspace{2em} x( 0 )= -5" title="{\left(t + 5\right)} {\left(t - 5\right)} {y} + t^{2} + 1 = -{\left(t + 2\right)} {y'} e^{t} \hspace{2em} x( 0 )= -5" data-latex="{\left(t + 5\right)} {\left(t - 5\right)} {y} + t^{2} + 1 = -{\left(t + 2\right)} {y'} e^{t} \hspace{2em} x( 0 )= -5"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-2,+\infty)" alt="(-2,+\infty)" title="(-2,+\infty)" data-latex="(-2,+\infty)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-2,+%5Cinfty)" alt="(-2,+\infty)" title="(-2,+\infty)" data-latex="(-2,+\infty)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-2433" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 2433"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?e^{\left(2 \, t\right)} = -{y'} {\left(t + 6\right)} {\left(t - 5\right)} - {y} t e^{t} \hspace{2em} x( 3 )= -9" alt="e^{\left(2 \, t\right)} = -{y'} {\left(t + 6\right)} {\left(t - 5\right)} - {y} t e^{t} \hspace{2em} x( 3 )= -9" title="e^{\left(2 \, t\right)} = -{y'} {\left(t + 6\right)} {\left(t - 5\right)} - {y} t e^{t} \hspace{2em} x( 3 )= -9" data-latex="e^{\left(2 \, t\right)} = -{y'} {\left(t + 6\right)} {\left(t - 5\right)} - {y} t e^{t} \hspace{2em} x( 3 )= -9"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?e%5E%7B%5Cleft(2%20%5C,%20t%5Cright)%7D%20=%20-%7By'%7D%20%7B%5Cleft(t%20+%206%5Cright)%7D%20%7B%5Cleft(t%20-%205%5Cright)%7D%20-%20%7By%7D%20t%20e%5E%7Bt%7D%20%5Chspace%7B2em%7D%20x(%203%20)=%20-9" alt="e^{\left(2 \, t\right)} = -{y'} {\left(t + 6\right)} {\left(t - 5\right)} - {y} t e^{t} \hspace{2em} x( 3 )= -9" title="e^{\left(2 \, t\right)} = -{y'} {\left(t + 6\right)} {\left(t - 5\right)} - {y} t e^{t} \hspace{2em} x( 3 )= -9" data-latex="e^{\left(2 \, t\right)} = -{y'} {\left(t + 6\right)} {\left(t - 5\right)} - {y} t e^{t} \hspace{2em} x( 3 )= -9"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-6,5)" alt="(-6,5)" title="(-6,5)" data-latex="(-6,5)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-6,5)" alt="(-6,5)" title="(-6,5)" data-latex="(-6,5)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-1204" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 1204"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{\left(t + 5\right)} {\left(t - 2\right)} {y'} = -t^{2} - {\left(t - 6\right)} {y} - 1 \hspace{2em} x( -2 )= 3" alt="{\left(t + 5\right)} {\left(t - 2\right)} {y'} = -t^{2} - {\left(t - 6\right)} {y} - 1 \hspace{2em} x( -2 )= 3" title="{\left(t + 5\right)} {\left(t - 2\right)} {y'} = -t^{2} - {\left(t - 6\right)} {y} - 1 \hspace{2em} x( -2 )= 3" data-latex="{\left(t + 5\right)} {\left(t - 2\right)} {y'} = -t^{2} - {\left(t - 6\right)} {y} - 1 \hspace{2em} x( -2 )= 3"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%7B%5Cleft(t%20+%205%5Cright)%7D%20%7B%5Cleft(t%20-%202%5Cright)%7D%20%7By'%7D%20=%20-t%5E%7B2%7D%20-%20%7B%5Cleft(t%20-%206%5Cright)%7D%20%7By%7D%20-%201%20%5Chspace%7B2em%7D%20x(%20-2%20)=%203" alt="{\left(t + 5\right)} {\left(t - 2\right)} {y'} = -t^{2} - {\left(t - 6\right)} {y} - 1 \hspace{2em} x( -2 )= 3" title="{\left(t + 5\right)} {\left(t - 2\right)} {y'} = -t^{2} - {\left(t - 6\right)} {y} - 1 \hspace{2em} x( -2 )= 3" data-latex="{\left(t + 5\right)} {\left(t - 2\right)} {y'} = -t^{2} - {\left(t - 6\right)} {y} - 1 \hspace{2em} x( -2 )= 3"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-5,2)" alt="(-5,2)" title="(-5,2)" data-latex="(-5,2)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-5,2)" alt="(-5,2)" title="(-5,2)" data-latex="(-5,2)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-7871" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 7871"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{\left(t^{2} + 25\right)} {y} = -{y'} {\left(t - 2\right)} - {\left(t + 5\right)} {\left(t - 5\right)} \hspace{2em} x( 6 )= -2" alt="{\left(t^{2} + 25\right)} {y} = -{y'} {\left(t - 2\right)} - {\left(t + 5\right)} {\left(t - 5\right)} \hspace{2em} x( 6 )= -2" title="{\left(t^{2} + 25\right)} {y} = -{y'} {\left(t - 2\right)} - {\left(t + 5\right)} {\left(t - 5\right)} \hspace{2em} x( 6 )= -2" data-latex="{\left(t^{2} + 25\right)} {y} = -{y'} {\left(t - 2\right)} - {\left(t + 5\right)} {\left(t - 5\right)} \hspace{2em} x( 6 )= -2"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%7B%5Cleft(t%5E%7B2%7D%20+%2025%5Cright)%7D%20%7By%7D%20=%20-%7By'%7D%20%7B%5Cleft(t%20-%202%5Cright)%7D%20-%20%7B%5Cleft(t%20+%205%5Cright)%7D%20%7B%5Cleft(t%20-%205%5Cright)%7D%20%5Chspace%7B2em%7D%20x(%206%20)=%20-2" alt="{\left(t^{2} + 25\right)} {y} = -{y'} {\left(t - 2\right)} - {\left(t + 5\right)} {\left(t - 5\right)} \hspace{2em} x( 6 )= -2" title="{\left(t^{2} + 25\right)} {y} = -{y'} {\left(t - 2\right)} - {\left(t + 5\right)} {\left(t - 5\right)} \hspace{2em} x( 6 )= -2" data-latex="{\left(t^{2} + 25\right)} {y} = -{y'} {\left(t - 2\right)} - {\left(t + 5\right)} {\left(t - 5\right)} \hspace{2em} x( 6 )= -2"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(2,+\infty)" alt="(2,+\infty)" title="(2,+\infty)" data-latex="(2,+\infty)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(2,+%5Cinfty)" alt="(2,+\infty)" title="(2,+\infty)" data-latex="(2,+\infty)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-8127" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 8127"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-{\left(t - 2\right)} {\left(t - 6\right)} {y} - e^{\left(-2 \, t\right)} = {\left(t + 6\right)} {y'} e^{t} \hspace{2em} x( -5 )= -10" alt="-{\left(t - 2\right)} {\left(t - 6\right)} {y} - e^{\left(-2 \, t\right)} = {\left(t + 6\right)} {y'} e^{t} \hspace{2em} x( -5 )= -10" title="-{\left(t - 2\right)} {\left(t - 6\right)} {y} - e^{\left(-2 \, t\right)} = {\left(t + 6\right)} {y'} e^{t} \hspace{2em} x( -5 )= -10" data-latex="-{\left(t - 2\right)} {\left(t - 6\right)} {y} - e^{\left(-2 \, t\right)} = {\left(t + 6\right)} {y'} e^{t} \hspace{2em} x( -5 )= -10"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-%7B%5Cleft(t%20-%202%5Cright)%7D%20%7B%5Cleft(t%20-%206%5Cright)%7D%20%7By%7D%20-%20e%5E%7B%5Cleft(-2%20%5C,%20t%5Cright)%7D%20=%20%7B%5Cleft(t%20+%206%5Cright)%7D%20%7By'%7D%20e%5E%7Bt%7D%20%5Chspace%7B2em%7D%20x(%20-5%20)=%20-10" alt="-{\left(t - 2\right)} {\left(t - 6\right)} {y} - e^{\left(-2 \, t\right)} = {\left(t + 6\right)} {y'} e^{t} \hspace{2em} x( -5 )= -10" title="-{\left(t - 2\right)} {\left(t - 6\right)} {y} - e^{\left(-2 \, t\right)} = {\left(t + 6\right)} {y'} e^{t} \hspace{2em} x( -5 )= -10" data-latex="-{\left(t - 2\right)} {\left(t - 6\right)} {y} - e^{\left(-2 \, t\right)} = {\left(t + 6\right)} {y'} e^{t} \hspace{2em} x( -5 )= -10"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-6,+\infty)" alt="(-6,+\infty)" title="(-6,+\infty)" data-latex="(-6,+\infty)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-6,+%5Cinfty)" alt="(-6,+\infty)" title="(-6,+\infty)" data-latex="(-6,+\infty)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-7248" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 7248"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-{\left(t + 5\right)} {\left(t + 1\right)} {y'} - {\left(t - 6\right)} e^{t} = {\left(t^{2} + 9\right)} {y} \hspace{2em} x( -2 )= 2" alt="-{\left(t + 5\right)} {\left(t + 1\right)} {y'} - {\left(t - 6\right)} e^{t} = {\left(t^{2} + 9\right)} {y} \hspace{2em} x( -2 )= 2" title="-{\left(t + 5\right)} {\left(t + 1\right)} {y'} - {\left(t - 6\right)} e^{t} = {\left(t^{2} + 9\right)} {y} \hspace{2em} x( -2 )= 2" data-latex="-{\left(t + 5\right)} {\left(t + 1\right)} {y'} - {\left(t - 6\right)} e^{t} = {\left(t^{2} + 9\right)} {y} \hspace{2em} x( -2 )= 2"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-%7B%5Cleft(t%20+%205%5Cright)%7D%20%7B%5Cleft(t%20+%201%5Cright)%7D%20%7By'%7D%20-%20%7B%5Cleft(t%20-%206%5Cright)%7D%20e%5E%7Bt%7D%20=%20%7B%5Cleft(t%5E%7B2%7D%20+%209%5Cright)%7D%20%7By%7D%20%5Chspace%7B2em%7D%20x(%20-2%20)=%202" alt="-{\left(t + 5\right)} {\left(t + 1\right)} {y'} - {\left(t - 6\right)} e^{t} = {\left(t^{2} + 9\right)} {y} \hspace{2em} x( -2 )= 2" title="-{\left(t + 5\right)} {\left(t + 1\right)} {y'} - {\left(t - 6\right)} e^{t} = {\left(t^{2} + 9\right)} {y} \hspace{2em} x( -2 )= 2" data-latex="-{\left(t + 5\right)} {\left(t + 1\right)} {y'} - {\left(t - 6\right)} e^{t} = {\left(t^{2} + 9\right)} {y} \hspace{2em} x( -2 )= 2"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-5,-1)" alt="(-5,-1)" title="(-5,-1)" data-latex="(-5,-1)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-5,-1)" alt="(-5,-1)" title="(-5,-1)" data-latex="(-5,-1)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-6866" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 6866"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-{y'} e^{\left(-4 \, t\right)} = {y} t e^{t} + {\left(t + 4\right)} {\left(t - 5\right)} \hspace{2em} x( -4 )= -4" alt="-{y'} e^{\left(-4 \, t\right)} = {y} t e^{t} + {\left(t + 4\right)} {\left(t - 5\right)} \hspace{2em} x( -4 )= -4" title="-{y'} e^{\left(-4 \, t\right)} = {y} t e^{t} + {\left(t + 4\right)} {\left(t - 5\right)} \hspace{2em} x( -4 )= -4" data-latex="-{y'} e^{\left(-4 \, t\right)} = {y} t e^{t} + {\left(t + 4\right)} {\left(t - 5\right)} \hspace{2em} x( -4 )= -4"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-%7By'%7D%20e%5E%7B%5Cleft(-4%20%5C,%20t%5Cright)%7D%20=%20%7By%7D%20t%20e%5E%7Bt%7D%20+%20%7B%5Cleft(t%20+%204%5Cright)%7D%20%7B%5Cleft(t%20-%205%5Cright)%7D%20%5Chspace%7B2em%7D%20x(%20-4%20)=%20-4" alt="-{y'} e^{\left(-4 \, t\right)} = {y} t e^{t} + {\left(t + 4\right)} {\left(t - 5\right)} \hspace{2em} x( -4 )= -4" title="-{y'} e^{\left(-4 \, t\right)} = {y} t e^{t} + {\left(t + 4\right)} {\left(t - 5\right)} \hspace{2em} x( -4 )= -4" data-latex="-{y'} e^{\left(-4 \, t\right)} = {y} t e^{t} + {\left(t + 4\right)} {\left(t - 5\right)} \hspace{2em} x( -4 )= -4"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-\infty,+\infty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-%5Cinfty,+%5Cinfty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-5140" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 5140"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?0 = {\left(t + 6\right)} {\left(t - 1\right)} {y'} + {\left(t - 5\right)} {y} e^{t} + t^{2} + 16 \hspace{2em} x( -4 )= 2" alt="0 = {\left(t + 6\right)} {\left(t - 1\right)} {y'} + {\left(t - 5\right)} {y} e^{t} + t^{2} + 16 \hspace{2em} x( -4 )= 2" title="0 = {\left(t + 6\right)} {\left(t - 1\right)} {y'} + {\left(t - 5\right)} {y} e^{t} + t^{2} + 16 \hspace{2em} x( -4 )= 2" data-latex="0 = {\left(t + 6\right)} {\left(t - 1\right)} {y'} + {\left(t - 5\right)} {y} e^{t} + t^{2} + 16 \hspace{2em} x( -4 )= 2"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?0%20=%20%7B%5Cleft(t%20+%206%5Cright)%7D%20%7B%5Cleft(t%20-%201%5Cright)%7D%20%7By'%7D%20+%20%7B%5Cleft(t%20-%205%5Cright)%7D%20%7By%7D%20e%5E%7Bt%7D%20+%20t%5E%7B2%7D%20+%2016%20%5Chspace%7B2em%7D%20x(%20-4%20)=%202" alt="0 = {\left(t + 6\right)} {\left(t - 1\right)} {y'} + {\left(t - 5\right)} {y} e^{t} + t^{2} + 16 \hspace{2em} x( -4 )= 2" title="0 = {\left(t + 6\right)} {\left(t - 1\right)} {y'} + {\left(t - 5\right)} {y} e^{t} + t^{2} + 16 \hspace{2em} x( -4 )= 2" data-latex="0 = {\left(t + 6\right)} {\left(t - 1\right)} {y'} + {\left(t - 5\right)} {y} e^{t} + t^{2} + 16 \hspace{2em} x( -4 )= 2"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-6,1)" alt="(-6,1)" title="(-6,1)" data-latex="(-6,1)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-6,1)" alt="(-6,1)" title="(-6,1)" data-latex="(-6,1)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-7514" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 7514"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-{\left(t + 5\right)} {\left(t - 6\right)} {y'} - {\left(t^{2} + 16\right)} {y} - t = 0 \hspace{2em} x( -1 )= -6" alt="-{\left(t + 5\right)} {\left(t - 6\right)} {y'} - {\left(t^{2} + 16\right)} {y} - t = 0 \hspace{2em} x( -1 )= -6" title="-{\left(t + 5\right)} {\left(t - 6\right)} {y'} - {\left(t^{2} + 16\right)} {y} - t = 0 \hspace{2em} x( -1 )= -6" data-latex="-{\left(t + 5\right)} {\left(t - 6\right)} {y'} - {\left(t^{2} + 16\right)} {y} - t = 0 \hspace{2em} x( -1 )= -6"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-%7B%5Cleft(t%20+%205%5Cright)%7D%20%7B%5Cleft(t%20-%206%5Cright)%7D%20%7By'%7D%20-%20%7B%5Cleft(t%5E%7B2%7D%20+%2016%5Cright)%7D%20%7By%7D%20-%20t%20=%200%20%5Chspace%7B2em%7D%20x(%20-1%20)=%20-6" alt="-{\left(t + 5\right)} {\left(t - 6\right)} {y'} - {\left(t^{2} + 16\right)} {y} - t = 0 \hspace{2em} x( -1 )= -6" title="-{\left(t + 5\right)} {\left(t - 6\right)} {y'} - {\left(t^{2} + 16\right)} {y} - t = 0 \hspace{2em} x( -1 )= -6" data-latex="-{\left(t + 5\right)} {\left(t - 6\right)} {y'} - {\left(t^{2} + 16\right)} {y} - t = 0 \hspace{2em} x( -1 )= -6"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-5,6)" alt="(-5,6)" title="(-5,6)" data-latex="(-5,6)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-5,6)" alt="(-5,6)" title="(-5,6)" data-latex="(-5,6)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-7754" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 7754"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-t - 5 = {y'} {\left(t - 1\right)} {\left(t - 6\right)} + {y} e^{\left(-4 \, t\right)} \hspace{2em} x( 3 )= 0" alt="-t - 5 = {y'} {\left(t - 1\right)} {\left(t - 6\right)} + {y} e^{\left(-4 \, t\right)} \hspace{2em} x( 3 )= 0" title="-t - 5 = {y'} {\left(t - 1\right)} {\left(t - 6\right)} + {y} e^{\left(-4 \, t\right)} \hspace{2em} x( 3 )= 0" data-latex="-t - 5 = {y'} {\left(t - 1\right)} {\left(t - 6\right)} + {y} e^{\left(-4 \, t\right)} \hspace{2em} x( 3 )= 0"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-t%20-%205%20=%20%7By'%7D%20%7B%5Cleft(t%20-%201%5Cright)%7D%20%7B%5Cleft(t%20-%206%5Cright)%7D%20+%20%7By%7D%20e%5E%7B%5Cleft(-4%20%5C,%20t%5Cright)%7D%20%5Chspace%7B2em%7D%20x(%203%20)=%200" alt="-t - 5 = {y'} {\left(t - 1\right)} {\left(t - 6\right)} + {y} e^{\left(-4 \, t\right)} \hspace{2em} x( 3 )= 0" title="-t - 5 = {y'} {\left(t - 1\right)} {\left(t - 6\right)} + {y} e^{\left(-4 \, t\right)} \hspace{2em} x( 3 )= 0" data-latex="-t - 5 = {y'} {\left(t - 1\right)} {\left(t - 6\right)} + {y} e^{\left(-4 \, t\right)} \hspace{2em} x( 3 )= 0"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(1,6)" alt="(1,6)" title="(1,6)" data-latex="(1,6)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(1,6)" alt="(1,6)" title="(1,6)" data-latex="(1,6)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-2437" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 2437"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-{\left(t - 6\right)} t = {y'} {\left(t + 4\right)} + {y} e^{\left(5 \, t\right)} \hspace{2em} x( 0 )= -5" alt="-{\left(t - 6\right)} t = {y'} {\left(t + 4\right)} + {y} e^{\left(5 \, t\right)} \hspace{2em} x( 0 )= -5" title="-{\left(t - 6\right)} t = {y'} {\left(t + 4\right)} + {y} e^{\left(5 \, t\right)} \hspace{2em} x( 0 )= -5" data-latex="-{\left(t - 6\right)} t = {y'} {\left(t + 4\right)} + {y} e^{\left(5 \, t\right)} \hspace{2em} x( 0 )= -5"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-%7B%5Cleft(t%20-%206%5Cright)%7D%20t%20=%20%7By'%7D%20%7B%5Cleft(t%20+%204%5Cright)%7D%20+%20%7By%7D%20e%5E%7B%5Cleft(5%20%5C,%20t%5Cright)%7D%20%5Chspace%7B2em%7D%20x(%200%20)=%20-5" alt="-{\left(t - 6\right)} t = {y'} {\left(t + 4\right)} + {y} e^{\left(5 \, t\right)} \hspace{2em} x( 0 )= -5" title="-{\left(t - 6\right)} t = {y'} {\left(t + 4\right)} + {y} e^{\left(5 \, t\right)} \hspace{2em} x( 0 )= -5" data-latex="-{\left(t - 6\right)} t = {y'} {\left(t + 4\right)} + {y} e^{\left(5 \, t\right)} \hspace{2em} x( 0 )= -5"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-4,+\infty)" alt="(-4,+\infty)" title="(-4,+\infty)" data-latex="(-4,+\infty)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-4,+%5Cinfty)" alt="(-4,+\infty)" title="(-4,+\infty)" data-latex="(-4,+\infty)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-1169" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 1169"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-{y} e^{\left(-t\right)} - {\left(t - 6\right)} e^{t} = {\left(t + 6\right)} {\left(t - 2\right)} {y'} \hspace{2em} x( 0 )= 3" alt="-{y} e^{\left(-t\right)} - {\left(t - 6\right)} e^{t} = {\left(t + 6\right)} {\left(t - 2\right)} {y'} \hspace{2em} x( 0 )= 3" title="-{y} e^{\left(-t\right)} - {\left(t - 6\right)} e^{t} = {\left(t + 6\right)} {\left(t - 2\right)} {y'} \hspace{2em} x( 0 )= 3" data-latex="-{y} e^{\left(-t\right)} - {\left(t - 6\right)} e^{t} = {\left(t + 6\right)} {\left(t - 2\right)} {y'} \hspace{2em} x( 0 )= 3"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-%7By%7D%20e%5E%7B%5Cleft(-t%5Cright)%7D%20-%20%7B%5Cleft(t%20-%206%5Cright)%7D%20e%5E%7Bt%7D%20=%20%7B%5Cleft(t%20+%206%5Cright)%7D%20%7B%5Cleft(t%20-%202%5Cright)%7D%20%7By'%7D%20%5Chspace%7B2em%7D%20x(%200%20)=%203" alt="-{y} e^{\left(-t\right)} - {\left(t - 6\right)} e^{t} = {\left(t + 6\right)} {\left(t - 2\right)} {y'} \hspace{2em} x( 0 )= 3" title="-{y} e^{\left(-t\right)} - {\left(t - 6\right)} e^{t} = {\left(t + 6\right)} {\left(t - 2\right)} {y'} \hspace{2em} x( 0 )= 3" data-latex="-{y} e^{\left(-t\right)} - {\left(t - 6\right)} e^{t} = {\left(t + 6\right)} {\left(t - 2\right)} {y'} \hspace{2em} x( 0 )= 3"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-6,2)" alt="(-6,2)" title="(-6,2)" data-latex="(-6,2)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-6,2)" alt="(-6,2)" title="(-6,2)" data-latex="(-6,2)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-7706" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 7706"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-t - 4 = {y'} {\left(t + 2\right)} {\left(t - 6\right)} + {y} e^{\left(-4 \, t\right)} \hspace{2em} x( 0 )= 8" alt="-t - 4 = {y'} {\left(t + 2\right)} {\left(t - 6\right)} + {y} e^{\left(-4 \, t\right)} \hspace{2em} x( 0 )= 8" title="-t - 4 = {y'} {\left(t + 2\right)} {\left(t - 6\right)} + {y} e^{\left(-4 \, t\right)} \hspace{2em} x( 0 )= 8" data-latex="-t - 4 = {y'} {\left(t + 2\right)} {\left(t - 6\right)} + {y} e^{\left(-4 \, t\right)} \hspace{2em} x( 0 )= 8"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-t%20-%204%20=%20%7By'%7D%20%7B%5Cleft(t%20+%202%5Cright)%7D%20%7B%5Cleft(t%20-%206%5Cright)%7D%20+%20%7By%7D%20e%5E%7B%5Cleft(-4%20%5C,%20t%5Cright)%7D%20%5Chspace%7B2em%7D%20x(%200%20)=%208" alt="-t - 4 = {y'} {\left(t + 2\right)} {\left(t - 6\right)} + {y} e^{\left(-4 \, t\right)} \hspace{2em} x( 0 )= 8" title="-t - 4 = {y'} {\left(t + 2\right)} {\left(t - 6\right)} + {y} e^{\left(-4 \, t\right)} \hspace{2em} x( 0 )= 8" data-latex="-t - 4 = {y'} {\left(t + 2\right)} {\left(t - 6\right)} + {y} e^{\left(-4 \, t\right)} \hspace{2em} x( 0 )= 8"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-2,6)" alt="(-2,6)" title="(-2,6)" data-latex="(-2,6)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-2,6)" alt="(-2,6)" title="(-2,6)" data-latex="(-2,6)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-8882" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 8882"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y} {\left(t + 4\right)} {\left(t + 1\right)} = -{y'} {\left(t - 5\right)} e^{t} - e^{\left(-5 \, t\right)} \hspace{2em} x( 2 )= 6" alt="{y} {\left(t + 4\right)} {\left(t + 1\right)} = -{y'} {\left(t - 5\right)} e^{t} - e^{\left(-5 \, t\right)} \hspace{2em} x( 2 )= 6" title="{y} {\left(t + 4\right)} {\left(t + 1\right)} = -{y'} {\left(t - 5\right)} e^{t} - e^{\left(-5 \, t\right)} \hspace{2em} x( 2 )= 6" data-latex="{y} {\left(t + 4\right)} {\left(t + 1\right)} = -{y'} {\left(t - 5\right)} e^{t} - e^{\left(-5 \, t\right)} \hspace{2em} x( 2 )= 6"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%7By%7D%20%7B%5Cleft(t%20+%204%5Cright)%7D%20%7B%5Cleft(t%20+%201%5Cright)%7D%20=%20-%7By'%7D%20%7B%5Cleft(t%20-%205%5Cright)%7D%20e%5E%7Bt%7D%20-%20e%5E%7B%5Cleft(-5%20%5C,%20t%5Cright)%7D%20%5Chspace%7B2em%7D%20x(%202%20)=%206" alt="{y} {\left(t + 4\right)} {\left(t + 1\right)} = -{y'} {\left(t - 5\right)} e^{t} - e^{\left(-5 \, t\right)} \hspace{2em} x( 2 )= 6" title="{y} {\left(t + 4\right)} {\left(t + 1\right)} = -{y'} {\left(t - 5\right)} e^{t} - e^{\left(-5 \, t\right)} \hspace{2em} x( 2 )= 6" data-latex="{y} {\left(t + 4\right)} {\left(t + 1\right)} = -{y'} {\left(t - 5\right)} e^{t} - e^{\left(-5 \, t\right)} \hspace{2em} x( 2 )= 6"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-\infty,5)" alt="(-\infty,5)" title="(-\infty,5)" data-latex="(-\infty,5)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-%5Cinfty,5)" alt="(-\infty,5)" title="(-\infty,5)" data-latex="(-\infty,5)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-8663" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 8663"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{\left(t + 2\right)} {\left(t - 5\right)} {y'} + {y} e^{\left(-5 \, t\right)} = -t - 4 \hspace{2em} x( 2 )= -5" alt="{\left(t + 2\right)} {\left(t - 5\right)} {y'} + {y} e^{\left(-5 \, t\right)} = -t - 4 \hspace{2em} x( 2 )= -5" title="{\left(t + 2\right)} {\left(t - 5\right)} {y'} + {y} e^{\left(-5 \, t\right)} = -t - 4 \hspace{2em} x( 2 )= -5" data-latex="{\left(t + 2\right)} {\left(t - 5\right)} {y'} + {y} e^{\left(-5 \, t\right)} = -t - 4 \hspace{2em} x( 2 )= -5"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%7B%5Cleft(t%20+%202%5Cright)%7D%20%7B%5Cleft(t%20-%205%5Cright)%7D%20%7By'%7D%20+%20%7By%7D%20e%5E%7B%5Cleft(-5%20%5C,%20t%5Cright)%7D%20=%20-t%20-%204%20%5Chspace%7B2em%7D%20x(%202%20)=%20-5" alt="{\left(t + 2\right)} {\left(t - 5\right)} {y'} + {y} e^{\left(-5 \, t\right)} = -t - 4 \hspace{2em} x( 2 )= -5" title="{\left(t + 2\right)} {\left(t - 5\right)} {y'} + {y} e^{\left(-5 \, t\right)} = -t - 4 \hspace{2em} x( 2 )= -5" data-latex="{\left(t + 2\right)} {\left(t - 5\right)} {y'} + {y} e^{\left(-5 \, t\right)} = -t - 4 \hspace{2em} x( 2 )= -5"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-2,5)" alt="(-2,5)" title="(-2,5)" data-latex="(-2,5)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-2,5)" alt="(-2,5)" title="(-2,5)" data-latex="(-2,5)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-9441" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 9441"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?0 = {\left(t + 5\right)} {\left(t + 2\right)} {y'} + {\left(t - 6\right)} {y} e^{t} + e^{t} \hspace{2em} x( -3 )= 2" alt="0 = {\left(t + 5\right)} {\left(t + 2\right)} {y'} + {\left(t - 6\right)} {y} e^{t} + e^{t} \hspace{2em} x( -3 )= 2" title="0 = {\left(t + 5\right)} {\left(t + 2\right)} {y'} + {\left(t - 6\right)} {y} e^{t} + e^{t} \hspace{2em} x( -3 )= 2" data-latex="0 = {\left(t + 5\right)} {\left(t + 2\right)} {y'} + {\left(t - 6\right)} {y} e^{t} + e^{t} \hspace{2em} x( -3 )= 2"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?0%20=%20%7B%5Cleft(t%20+%205%5Cright)%7D%20%7B%5Cleft(t%20+%202%5Cright)%7D%20%7By'%7D%20+%20%7B%5Cleft(t%20-%206%5Cright)%7D%20%7By%7D%20e%5E%7Bt%7D%20+%20e%5E%7Bt%7D%20%5Chspace%7B2em%7D%20x(%20-3%20)=%202" alt="0 = {\left(t + 5\right)} {\left(t + 2\right)} {y'} + {\left(t - 6\right)} {y} e^{t} + e^{t} \hspace{2em} x( -3 )= 2" title="0 = {\left(t + 5\right)} {\left(t + 2\right)} {y'} + {\left(t - 6\right)} {y} e^{t} + e^{t} \hspace{2em} x( -3 )= 2" data-latex="0 = {\left(t + 5\right)} {\left(t + 2\right)} {y'} + {\left(t - 6\right)} {y} e^{t} + e^{t} \hspace{2em} x( -3 )= 2"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-5,-2)" alt="(-5,-2)" title="(-5,-2)" data-latex="(-5,-2)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-5,-2)" alt="(-5,-2)" title="(-5,-2)" data-latex="(-5,-2)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-6599" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 6599"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?e^{\left(5 \, t\right)} = -{y'} {\left(t + 6\right)} {\left(t - 1\right)} - {y} {\left(t - 6\right)} e^{t} \hspace{2em} x( -1 )= 4" alt="e^{\left(5 \, t\right)} = -{y'} {\left(t + 6\right)} {\left(t - 1\right)} - {y} {\left(t - 6\right)} e^{t} \hspace{2em} x( -1 )= 4" title="e^{\left(5 \, t\right)} = -{y'} {\left(t + 6\right)} {\left(t - 1\right)} - {y} {\left(t - 6\right)} e^{t} \hspace{2em} x( -1 )= 4" data-latex="e^{\left(5 \, t\right)} = -{y'} {\left(t + 6\right)} {\left(t - 1\right)} - {y} {\left(t - 6\right)} e^{t} \hspace{2em} x( -1 )= 4"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?e%5E%7B%5Cleft(5%20%5C,%20t%5Cright)%7D%20=%20-%7By'%7D%20%7B%5Cleft(t%20+%206%5Cright)%7D%20%7B%5Cleft(t%20-%201%5Cright)%7D%20-%20%7By%7D%20%7B%5Cleft(t%20-%206%5Cright)%7D%20e%5E%7Bt%7D%20%5Chspace%7B2em%7D%20x(%20-1%20)=%204" alt="e^{\left(5 \, t\right)} = -{y'} {\left(t + 6\right)} {\left(t - 1\right)} - {y} {\left(t - 6\right)} e^{t} \hspace{2em} x( -1 )= 4" title="e^{\left(5 \, t\right)} = -{y'} {\left(t + 6\right)} {\left(t - 1\right)} - {y} {\left(t - 6\right)} e^{t} \hspace{2em} x( -1 )= 4" data-latex="e^{\left(5 \, t\right)} = -{y'} {\left(t + 6\right)} {\left(t - 1\right)} - {y} {\left(t - 6\right)} e^{t} \hspace{2em} x( -1 )= 4"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-6,1)" alt="(-6,1)" title="(-6,1)" data-latex="(-6,1)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-6,1)" alt="(-6,1)" title="(-6,1)" data-latex="(-6,1)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-5562" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 5562"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y} {\left(t + 5\right)} = -{y'} {\left(t - 1\right)} {\left(t - 6\right)} - t^{2} - 16 \hspace{2em} x( 4 )= 8" alt="{y} {\left(t + 5\right)} = -{y'} {\left(t - 1\right)} {\left(t - 6\right)} - t^{2} - 16 \hspace{2em} x( 4 )= 8" title="{y} {\left(t + 5\right)} = -{y'} {\left(t - 1\right)} {\left(t - 6\right)} - t^{2} - 16 \hspace{2em} x( 4 )= 8" data-latex="{y} {\left(t + 5\right)} = -{y'} {\left(t - 1\right)} {\left(t - 6\right)} - t^{2} - 16 \hspace{2em} x( 4 )= 8"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%7By%7D%20%7B%5Cleft(t%20+%205%5Cright)%7D%20=%20-%7By'%7D%20%7B%5Cleft(t%20-%201%5Cright)%7D%20%7B%5Cleft(t%20-%206%5Cright)%7D%20-%20t%5E%7B2%7D%20-%2016%20%5Chspace%7B2em%7D%20x(%204%20)=%208" alt="{y} {\left(t + 5\right)} = -{y'} {\left(t - 1\right)} {\left(t - 6\right)} - t^{2} - 16 \hspace{2em} x( 4 )= 8" title="{y} {\left(t + 5\right)} = -{y'} {\left(t - 1\right)} {\left(t - 6\right)} - t^{2} - 16 \hspace{2em} x( 4 )= 8" data-latex="{y} {\left(t + 5\right)} = -{y'} {\left(t - 1\right)} {\left(t - 6\right)} - t^{2} - 16 \hspace{2em} x( 4 )= 8"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(1,6)" alt="(1,6)" title="(1,6)" data-latex="(1,6)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(1,6)" alt="(1,6)" title="(1,6)" data-latex="(1,6)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-1353" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 1353"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-{y'} {\left(t + 2\right)} e^{t} - {\left(t^{2} + 1\right)} {y} - {\left(t + 4\right)} {\left(t - 5\right)} = 0 \hspace{2em} x( -5 )= 1" alt="-{y'} {\left(t + 2\right)} e^{t} - {\left(t^{2} + 1\right)} {y} - {\left(t + 4\right)} {\left(t - 5\right)} = 0 \hspace{2em} x( -5 )= 1" title="-{y'} {\left(t + 2\right)} e^{t} - {\left(t^{2} + 1\right)} {y} - {\left(t + 4\right)} {\left(t - 5\right)} = 0 \hspace{2em} x( -5 )= 1" data-latex="-{y'} {\left(t + 2\right)} e^{t} - {\left(t^{2} + 1\right)} {y} - {\left(t + 4\right)} {\left(t - 5\right)} = 0 \hspace{2em} x( -5 )= 1"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-%7By'%7D%20%7B%5Cleft(t%20+%202%5Cright)%7D%20e%5E%7Bt%7D%20-%20%7B%5Cleft(t%5E%7B2%7D%20+%201%5Cright)%7D%20%7By%7D%20-%20%7B%5Cleft(t%20+%204%5Cright)%7D%20%7B%5Cleft(t%20-%205%5Cright)%7D%20=%200%20%5Chspace%7B2em%7D%20x(%20-5%20)=%201" alt="-{y'} {\left(t + 2\right)} e^{t} - {\left(t^{2} + 1\right)} {y} - {\left(t + 4\right)} {\left(t - 5\right)} = 0 \hspace{2em} x( -5 )= 1" title="-{y'} {\left(t + 2\right)} e^{t} - {\left(t^{2} + 1\right)} {y} - {\left(t + 4\right)} {\left(t - 5\right)} = 0 \hspace{2em} x( -5 )= 1" data-latex="-{y'} {\left(t + 2\right)} e^{t} - {\left(t^{2} + 1\right)} {y} - {\left(t + 4\right)} {\left(t - 5\right)} = 0 \hspace{2em} x( -5 )= 1"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-\infty,-2)" alt="(-\infty,-2)" title="(-\infty,-2)" data-latex="(-\infty,-2)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-%5Cinfty,-2)" alt="(-\infty,-2)" title="(-\infty,-2)" data-latex="(-\infty,-2)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-4122" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 4122"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?0 = {\left(t + 4\right)} t {y} + t^{2} + {\left(t - 6\right)} {y'} + 4 \hspace{2em} x( 4 )= 9" alt="0 = {\left(t + 4\right)} t {y} + t^{2} + {\left(t - 6\right)} {y'} + 4 \hspace{2em} x( 4 )= 9" title="0 = {\left(t + 4\right)} t {y} + t^{2} + {\left(t - 6\right)} {y'} + 4 \hspace{2em} x( 4 )= 9" data-latex="0 = {\left(t + 4\right)} t {y} + t^{2} + {\left(t - 6\right)} {y'} + 4 \hspace{2em} x( 4 )= 9"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?0%20=%20%7B%5Cleft(t%20+%204%5Cright)%7D%20t%20%7By%7D%20+%20t%5E%7B2%7D%20+%20%7B%5Cleft(t%20-%206%5Cright)%7D%20%7By'%7D%20+%204%20%5Chspace%7B2em%7D%20x(%204%20)=%209" alt="0 = {\left(t + 4\right)} t {y} + t^{2} + {\left(t - 6\right)} {y'} + 4 \hspace{2em} x( 4 )= 9" title="0 = {\left(t + 4\right)} t {y} + t^{2} + {\left(t - 6\right)} {y'} + 4 \hspace{2em} x( 4 )= 9" data-latex="0 = {\left(t + 4\right)} t {y} + t^{2} + {\left(t - 6\right)} {y'} + 4 \hspace{2em} x( 4 )= 9"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-\infty,6)" alt="(-\infty,6)" title="(-\infty,6)" data-latex="(-\infty,6)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-%5Cinfty,6)" alt="(-\infty,6)" title="(-\infty,6)" data-latex="(-\infty,6)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-1550" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 1550"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y'} {\left(t + 6\right)} t + t - 5 = -{\left(t^{2} + 1\right)} {y} \hspace{2em} x( -5 )= -10" alt="{y'} {\left(t + 6\right)} t + t - 5 = -{\left(t^{2} + 1\right)} {y} \hspace{2em} x( -5 )= -10" title="{y'} {\left(t + 6\right)} t + t - 5 = -{\left(t^{2} + 1\right)} {y} \hspace{2em} x( -5 )= -10" data-latex="{y'} {\left(t + 6\right)} t + t - 5 = -{\left(t^{2} + 1\right)} {y} \hspace{2em} x( -5 )= -10"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%7By'%7D%20%7B%5Cleft(t%20+%206%5Cright)%7D%20t%20+%20t%20-%205%20=%20-%7B%5Cleft(t%5E%7B2%7D%20+%201%5Cright)%7D%20%7By%7D%20%5Chspace%7B2em%7D%20x(%20-5%20)=%20-10" alt="{y'} {\left(t + 6\right)} t + t - 5 = -{\left(t^{2} + 1\right)} {y} \hspace{2em} x( -5 )= -10" title="{y'} {\left(t + 6\right)} t + t - 5 = -{\left(t^{2} + 1\right)} {y} \hspace{2em} x( -5 )= -10" data-latex="{y'} {\left(t + 6\right)} t + t - 5 = -{\left(t^{2} + 1\right)} {y} \hspace{2em} x( -5 )= -10"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-6,0)" alt="(-6,0)" title="(-6,0)" data-latex="(-6,0)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-6,0)" alt="(-6,0)" title="(-6,0)" data-latex="(-6,0)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-2340" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 2340"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-{\left(t - 2\right)} {\left(t - 5\right)} = {\left(t + 5\right)} {y} e^{t} + {y'} e^{\left(-2 \, t\right)} \hspace{2em} x( -2 )= -5" alt="-{\left(t - 2\right)} {\left(t - 5\right)} = {\left(t + 5\right)} {y} e^{t} + {y'} e^{\left(-2 \, t\right)} \hspace{2em} x( -2 )= -5" title="-{\left(t - 2\right)} {\left(t - 5\right)} = {\left(t + 5\right)} {y} e^{t} + {y'} e^{\left(-2 \, t\right)} \hspace{2em} x( -2 )= -5" data-latex="-{\left(t - 2\right)} {\left(t - 5\right)} = {\left(t + 5\right)} {y} e^{t} + {y'} e^{\left(-2 \, t\right)} \hspace{2em} x( -2 )= -5"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-%7B%5Cleft(t%20-%202%5Cright)%7D%20%7B%5Cleft(t%20-%205%5Cright)%7D%20=%20%7B%5Cleft(t%20+%205%5Cright)%7D%20%7By%7D%20e%5E%7Bt%7D%20+%20%7By'%7D%20e%5E%7B%5Cleft(-2%20%5C,%20t%5Cright)%7D%20%5Chspace%7B2em%7D%20x(%20-2%20)=%20-5" alt="-{\left(t - 2\right)} {\left(t - 5\right)} = {\left(t + 5\right)} {y} e^{t} + {y'} e^{\left(-2 \, t\right)} \hspace{2em} x( -2 )= -5" title="-{\left(t - 2\right)} {\left(t - 5\right)} = {\left(t + 5\right)} {y} e^{t} + {y'} e^{\left(-2 \, t\right)} \hspace{2em} x( -2 )= -5" data-latex="-{\left(t - 2\right)} {\left(t - 5\right)} = {\left(t + 5\right)} {y} e^{t} + {y'} e^{\left(-2 \, t\right)} \hspace{2em} x( -2 )= -5"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-\infty,+\infty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-%5Cinfty,+%5Cinfty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-0325" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 0325"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-t - 4 = {\left(t + 1\right)} {\left(t - 5\right)} {y} + {\left(t^{2} + 16\right)} {y'} \hspace{2em} x( 3 )= -3" alt="-t - 4 = {\left(t + 1\right)} {\left(t - 5\right)} {y} + {\left(t^{2} + 16\right)} {y'} \hspace{2em} x( 3 )= -3" title="-t - 4 = {\left(t + 1\right)} {\left(t - 5\right)} {y} + {\left(t^{2} + 16\right)} {y'} \hspace{2em} x( 3 )= -3" data-latex="-t - 4 = {\left(t + 1\right)} {\left(t - 5\right)} {y} + {\left(t^{2} + 16\right)} {y'} \hspace{2em} x( 3 )= -3"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-t%20-%204%20=%20%7B%5Cleft(t%20+%201%5Cright)%7D%20%7B%5Cleft(t%20-%205%5Cright)%7D%20%7By%7D%20+%20%7B%5Cleft(t%5E%7B2%7D%20+%2016%5Cright)%7D%20%7By'%7D%20%5Chspace%7B2em%7D%20x(%203%20)=%20-3" alt="-t - 4 = {\left(t + 1\right)} {\left(t - 5\right)} {y} + {\left(t^{2} + 16\right)} {y'} \hspace{2em} x( 3 )= -3" title="-t - 4 = {\left(t + 1\right)} {\left(t - 5\right)} {y} + {\left(t^{2} + 16\right)} {y'} \hspace{2em} x( 3 )= -3" data-latex="-t - 4 = {\left(t + 1\right)} {\left(t - 5\right)} {y} + {\left(t^{2} + 16\right)} {y'} \hspace{2em} x( 3 )= -3"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-\infty,+\infty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-%5Cinfty,+%5Cinfty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-6778" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 6778"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y} {\left(t - 6\right)} + e^{\left(5 \, t\right)} = -{y'} {\left(t + 5\right)} {\left(t - 2\right)} \hspace{2em} x( -1 )= 6" alt="{y} {\left(t - 6\right)} + e^{\left(5 \, t\right)} = -{y'} {\left(t + 5\right)} {\left(t - 2\right)} \hspace{2em} x( -1 )= 6" title="{y} {\left(t - 6\right)} + e^{\left(5 \, t\right)} = -{y'} {\left(t + 5\right)} {\left(t - 2\right)} \hspace{2em} x( -1 )= 6" data-latex="{y} {\left(t - 6\right)} + e^{\left(5 \, t\right)} = -{y'} {\left(t + 5\right)} {\left(t - 2\right)} \hspace{2em} x( -1 )= 6"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%7By%7D%20%7B%5Cleft(t%20-%206%5Cright)%7D%20+%20e%5E%7B%5Cleft(5%20%5C,%20t%5Cright)%7D%20=%20-%7By'%7D%20%7B%5Cleft(t%20+%205%5Cright)%7D%20%7B%5Cleft(t%20-%202%5Cright)%7D%20%5Chspace%7B2em%7D%20x(%20-1%20)=%206" alt="{y} {\left(t - 6\right)} + e^{\left(5 \, t\right)} = -{y'} {\left(t + 5\right)} {\left(t - 2\right)} \hspace{2em} x( -1 )= 6" title="{y} {\left(t - 6\right)} + e^{\left(5 \, t\right)} = -{y'} {\left(t + 5\right)} {\left(t - 2\right)} \hspace{2em} x( -1 )= 6" data-latex="{y} {\left(t - 6\right)} + e^{\left(5 \, t\right)} = -{y'} {\left(t + 5\right)} {\left(t - 2\right)} \hspace{2em} x( -1 )= 6"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-5,2)" alt="(-5,2)" title="(-5,2)" data-latex="(-5,2)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-5,2)" alt="(-5,2)" title="(-5,2)" data-latex="(-5,2)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-1117" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 1117"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-{\left(t + 1\right)} {y} = {\left(t + 5\right)} {\left(t - 5\right)} + {y'} e^{\left(-5 \, t\right)} \hspace{2em} x( -2 )= -4" alt="-{\left(t + 1\right)} {y} = {\left(t + 5\right)} {\left(t - 5\right)} + {y'} e^{\left(-5 \, t\right)} \hspace{2em} x( -2 )= -4" title="-{\left(t + 1\right)} {y} = {\left(t + 5\right)} {\left(t - 5\right)} + {y'} e^{\left(-5 \, t\right)} \hspace{2em} x( -2 )= -4" data-latex="-{\left(t + 1\right)} {y} = {\left(t + 5\right)} {\left(t - 5\right)} + {y'} e^{\left(-5 \, t\right)} \hspace{2em} x( -2 )= -4"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-%7B%5Cleft(t%20+%201%5Cright)%7D%20%7By%7D%20=%20%7B%5Cleft(t%20+%205%5Cright)%7D%20%7B%5Cleft(t%20-%205%5Cright)%7D%20+%20%7By'%7D%20e%5E%7B%5Cleft(-5%20%5C,%20t%5Cright)%7D%20%5Chspace%7B2em%7D%20x(%20-2%20)=%20-4" alt="-{\left(t + 1\right)} {y} = {\left(t + 5\right)} {\left(t - 5\right)} + {y'} e^{\left(-5 \, t\right)} \hspace{2em} x( -2 )= -4" title="-{\left(t + 1\right)} {y} = {\left(t + 5\right)} {\left(t - 5\right)} + {y'} e^{\left(-5 \, t\right)} \hspace{2em} x( -2 )= -4" data-latex="-{\left(t + 1\right)} {y} = {\left(t + 5\right)} {\left(t - 5\right)} + {y'} e^{\left(-5 \, t\right)} \hspace{2em} x( -2 )= -4"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-\infty,+\infty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-%5Cinfty,+%5Cinfty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-5579" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 5579"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{\left(t + 6\right)} {\left(t - 6\right)} + {y'} e^{\left(2 \, t\right)} = -{\left(t + 2\right)} {y} \hspace{2em} x( 1 )= -4" alt="{\left(t + 6\right)} {\left(t - 6\right)} + {y'} e^{\left(2 \, t\right)} = -{\left(t + 2\right)} {y} \hspace{2em} x( 1 )= -4" title="{\left(t + 6\right)} {\left(t - 6\right)} + {y'} e^{\left(2 \, t\right)} = -{\left(t + 2\right)} {y} \hspace{2em} x( 1 )= -4" data-latex="{\left(t + 6\right)} {\left(t - 6\right)} + {y'} e^{\left(2 \, t\right)} = -{\left(t + 2\right)} {y} \hspace{2em} x( 1 )= -4"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%7B%5Cleft(t%20+%206%5Cright)%7D%20%7B%5Cleft(t%20-%206%5Cright)%7D%20+%20%7By'%7D%20e%5E%7B%5Cleft(2%20%5C,%20t%5Cright)%7D%20=%20-%7B%5Cleft(t%20+%202%5Cright)%7D%20%7By%7D%20%5Chspace%7B2em%7D%20x(%201%20)=%20-4" alt="{\left(t + 6\right)} {\left(t - 6\right)} + {y'} e^{\left(2 \, t\right)} = -{\left(t + 2\right)} {y} \hspace{2em} x( 1 )= -4" title="{\left(t + 6\right)} {\left(t - 6\right)} + {y'} e^{\left(2 \, t\right)} = -{\left(t + 2\right)} {y} \hspace{2em} x( 1 )= -4" data-latex="{\left(t + 6\right)} {\left(t - 6\right)} + {y'} e^{\left(2 \, t\right)} = -{\left(t + 2\right)} {y} \hspace{2em} x( 1 )= -4"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-\infty,+\infty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-%5Cinfty,+%5Cinfty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-8383" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 8383"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-{\left(t - 1\right)} {y} = {\left(t + 6\right)} {\left(t - 5\right)} {y'} + t^{2} + 9 \hspace{2em} x( 2 )= 6" alt="-{\left(t - 1\right)} {y} = {\left(t + 6\right)} {\left(t - 5\right)} {y'} + t^{2} + 9 \hspace{2em} x( 2 )= 6" title="-{\left(t - 1\right)} {y} = {\left(t + 6\right)} {\left(t - 5\right)} {y'} + t^{2} + 9 \hspace{2em} x( 2 )= 6" data-latex="-{\left(t - 1\right)} {y} = {\left(t + 6\right)} {\left(t - 5\right)} {y'} + t^{2} + 9 \hspace{2em} x( 2 )= 6"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-%7B%5Cleft(t%20-%201%5Cright)%7D%20%7By%7D%20=%20%7B%5Cleft(t%20+%206%5Cright)%7D%20%7B%5Cleft(t%20-%205%5Cright)%7D%20%7By'%7D%20+%20t%5E%7B2%7D%20+%209%20%5Chspace%7B2em%7D%20x(%202%20)=%206" alt="-{\left(t - 1\right)} {y} = {\left(t + 6\right)} {\left(t - 5\right)} {y'} + t^{2} + 9 \hspace{2em} x( 2 )= 6" title="-{\left(t - 1\right)} {y} = {\left(t + 6\right)} {\left(t - 5\right)} {y'} + t^{2} + 9 \hspace{2em} x( 2 )= 6" data-latex="-{\left(t - 1\right)} {y} = {\left(t + 6\right)} {\left(t - 5\right)} {y'} + t^{2} + 9 \hspace{2em} x( 2 )= 6"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-6,5)" alt="(-6,5)" title="(-6,5)" data-latex="(-6,5)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-6,5)" alt="(-6,5)" title="(-6,5)" data-latex="(-6,5)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-2163" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 2163"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y} {\left(t - 1\right)} {\left(t - 6\right)} + {y'} {\left(t + 5\right)} e^{t} + e^{\left(-4 \, t\right)} = 0 \hspace{2em} x( -6 )= -4" alt="{y} {\left(t - 1\right)} {\left(t - 6\right)} + {y'} {\left(t + 5\right)} e^{t} + e^{\left(-4 \, t\right)} = 0 \hspace{2em} x( -6 )= -4" title="{y} {\left(t - 1\right)} {\left(t - 6\right)} + {y'} {\left(t + 5\right)} e^{t} + e^{\left(-4 \, t\right)} = 0 \hspace{2em} x( -6 )= -4" data-latex="{y} {\left(t - 1\right)} {\left(t - 6\right)} + {y'} {\left(t + 5\right)} e^{t} + e^{\left(-4 \, t\right)} = 0 \hspace{2em} x( -6 )= -4"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%7By%7D%20%7B%5Cleft(t%20-%201%5Cright)%7D%20%7B%5Cleft(t%20-%206%5Cright)%7D%20+%20%7By'%7D%20%7B%5Cleft(t%20+%205%5Cright)%7D%20e%5E%7Bt%7D%20+%20e%5E%7B%5Cleft(-4%20%5C,%20t%5Cright)%7D%20=%200%20%5Chspace%7B2em%7D%20x(%20-6%20)=%20-4" alt="{y} {\left(t - 1\right)} {\left(t - 6\right)} + {y'} {\left(t + 5\right)} e^{t} + e^{\left(-4 \, t\right)} = 0 \hspace{2em} x( -6 )= -4" title="{y} {\left(t - 1\right)} {\left(t - 6\right)} + {y'} {\left(t + 5\right)} e^{t} + e^{\left(-4 \, t\right)} = 0 \hspace{2em} x( -6 )= -4" data-latex="{y} {\left(t - 1\right)} {\left(t - 6\right)} + {y'} {\left(t + 5\right)} e^{t} + e^{\left(-4 \, t\right)} = 0 \hspace{2em} x( -6 )= -4"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-\infty,-5)" alt="(-\infty,-5)" title="(-\infty,-5)" data-latex="(-\infty,-5)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-%5Cinfty,-5)" alt="(-\infty,-5)" title="(-\infty,-5)" data-latex="(-\infty,-5)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-0857" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 0857"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y'} e^{\left(4 \, t\right)} + {\left(t + 6\right)} e^{t} = -{\left(t - 6\right)} t {y} \hspace{2em} x( -3 )= -1" alt="{y'} e^{\left(4 \, t\right)} + {\left(t + 6\right)} e^{t} = -{\left(t - 6\right)} t {y} \hspace{2em} x( -3 )= -1" title="{y'} e^{\left(4 \, t\right)} + {\left(t + 6\right)} e^{t} = -{\left(t - 6\right)} t {y} \hspace{2em} x( -3 )= -1" data-latex="{y'} e^{\left(4 \, t\right)} + {\left(t + 6\right)} e^{t} = -{\left(t - 6\right)} t {y} \hspace{2em} x( -3 )= -1"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%7By'%7D%20e%5E%7B%5Cleft(4%20%5C,%20t%5Cright)%7D%20+%20%7B%5Cleft(t%20+%206%5Cright)%7D%20e%5E%7Bt%7D%20=%20-%7B%5Cleft(t%20-%206%5Cright)%7D%20t%20%7By%7D%20%5Chspace%7B2em%7D%20x(%20-3%20)=%20-1" alt="{y'} e^{\left(4 \, t\right)} + {\left(t + 6\right)} e^{t} = -{\left(t - 6\right)} t {y} \hspace{2em} x( -3 )= -1" title="{y'} e^{\left(4 \, t\right)} + {\left(t + 6\right)} e^{t} = -{\left(t - 6\right)} t {y} \hspace{2em} x( -3 )= -1" data-latex="{y'} e^{\left(4 \, t\right)} + {\left(t + 6\right)} e^{t} = -{\left(t - 6\right)} t {y} \hspace{2em} x( -3 )= -1"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-\infty,+\infty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-%5Cinfty,+%5Cinfty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-0966" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 0966"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{\left(t^{2} + 25\right)} {y'} + {\left(t + 2\right)} {\left(t - 5\right)} = -{y} {\left(t + 5\right)} \hspace{2em} x( -3 )= -6" alt="{\left(t^{2} + 25\right)} {y'} + {\left(t + 2\right)} {\left(t - 5\right)} = -{y} {\left(t + 5\right)} \hspace{2em} x( -3 )= -6" title="{\left(t^{2} + 25\right)} {y'} + {\left(t + 2\right)} {\left(t - 5\right)} = -{y} {\left(t + 5\right)} \hspace{2em} x( -3 )= -6" data-latex="{\left(t^{2} + 25\right)} {y'} + {\left(t + 2\right)} {\left(t - 5\right)} = -{y} {\left(t + 5\right)} \hspace{2em} x( -3 )= -6"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%7B%5Cleft(t%5E%7B2%7D%20+%2025%5Cright)%7D%20%7By'%7D%20+%20%7B%5Cleft(t%20+%202%5Cright)%7D%20%7B%5Cleft(t%20-%205%5Cright)%7D%20=%20-%7By%7D%20%7B%5Cleft(t%20+%205%5Cright)%7D%20%5Chspace%7B2em%7D%20x(%20-3%20)=%20-6" alt="{\left(t^{2} + 25\right)} {y'} + {\left(t + 2\right)} {\left(t - 5\right)} = -{y} {\left(t + 5\right)} \hspace{2em} x( -3 )= -6" title="{\left(t^{2} + 25\right)} {y'} + {\left(t + 2\right)} {\left(t - 5\right)} = -{y} {\left(t + 5\right)} \hspace{2em} x( -3 )= -6" data-latex="{\left(t^{2} + 25\right)} {y'} + {\left(t + 2\right)} {\left(t - 5\right)} = -{y} {\left(t + 5\right)} \hspace{2em} x( -3 )= -6"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-\infty,+\infty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-%5Cinfty,+%5Cinfty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-4311" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 4311"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y'} {\left(t + 5\right)} {\left(t - 6\right)} + {y} {\left(t - 2\right)} = -t^{2} - 4 \hspace{2em} x( 2 )= -8" alt="{y'} {\left(t + 5\right)} {\left(t - 6\right)} + {y} {\left(t - 2\right)} = -t^{2} - 4 \hspace{2em} x( 2 )= -8" title="{y'} {\left(t + 5\right)} {\left(t - 6\right)} + {y} {\left(t - 2\right)} = -t^{2} - 4 \hspace{2em} x( 2 )= -8" data-latex="{y'} {\left(t + 5\right)} {\left(t - 6\right)} + {y} {\left(t - 2\right)} = -t^{2} - 4 \hspace{2em} x( 2 )= -8"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%7By'%7D%20%7B%5Cleft(t%20+%205%5Cright)%7D%20%7B%5Cleft(t%20-%206%5Cright)%7D%20+%20%7By%7D%20%7B%5Cleft(t%20-%202%5Cright)%7D%20=%20-t%5E%7B2%7D%20-%204%20%5Chspace%7B2em%7D%20x(%202%20)=%20-8" alt="{y'} {\left(t + 5\right)} {\left(t - 6\right)} + {y} {\left(t - 2\right)} = -t^{2} - 4 \hspace{2em} x( 2 )= -8" title="{y'} {\left(t + 5\right)} {\left(t - 6\right)} + {y} {\left(t - 2\right)} = -t^{2} - 4 \hspace{2em} x( 2 )= -8" data-latex="{y'} {\left(t + 5\right)} {\left(t - 6\right)} + {y} {\left(t - 2\right)} = -t^{2} - 4 \hspace{2em} x( 2 )= -8"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-5,6)" alt="(-5,6)" title="(-5,6)" data-latex="(-5,6)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-5,6)" alt="(-5,6)" title="(-5,6)" data-latex="(-5,6)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-0672" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 0672"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y} {\left(t + 1\right)} e^{t} + {y'} e^{\left(2 \, t\right)} = -{\left(t + 5\right)} {\left(t - 5\right)} \hspace{2em} x( -3 )= -2" alt="{y} {\left(t + 1\right)} e^{t} + {y'} e^{\left(2 \, t\right)} = -{\left(t + 5\right)} {\left(t - 5\right)} \hspace{2em} x( -3 )= -2" title="{y} {\left(t + 1\right)} e^{t} + {y'} e^{\left(2 \, t\right)} = -{\left(t + 5\right)} {\left(t - 5\right)} \hspace{2em} x( -3 )= -2" data-latex="{y} {\left(t + 1\right)} e^{t} + {y'} e^{\left(2 \, t\right)} = -{\left(t + 5\right)} {\left(t - 5\right)} \hspace{2em} x( -3 )= -2"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%7By%7D%20%7B%5Cleft(t%20+%201%5Cright)%7D%20e%5E%7Bt%7D%20+%20%7By'%7D%20e%5E%7B%5Cleft(2%20%5C,%20t%5Cright)%7D%20=%20-%7B%5Cleft(t%20+%205%5Cright)%7D%20%7B%5Cleft(t%20-%205%5Cright)%7D%20%5Chspace%7B2em%7D%20x(%20-3%20)=%20-2" alt="{y} {\left(t + 1\right)} e^{t} + {y'} e^{\left(2 \, t\right)} = -{\left(t + 5\right)} {\left(t - 5\right)} \hspace{2em} x( -3 )= -2" title="{y} {\left(t + 1\right)} e^{t} + {y'} e^{\left(2 \, t\right)} = -{\left(t + 5\right)} {\left(t - 5\right)} \hspace{2em} x( -3 )= -2" data-latex="{y} {\left(t + 1\right)} e^{t} + {y'} e^{\left(2 \, t\right)} = -{\left(t + 5\right)} {\left(t - 5\right)} \hspace{2em} x( -3 )= -2"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-\infty,+\infty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-%5Cinfty,+%5Cinfty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-3341" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 3341"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{\left(t + 5\right)} {\left(t - 5\right)} = -{y'} {\left(t - 1\right)} e^{t} - {\left(t^{2} + 16\right)} {y} \hspace{2em} x( -3 )= 2" alt="{\left(t + 5\right)} {\left(t - 5\right)} = -{y'} {\left(t - 1\right)} e^{t} - {\left(t^{2} + 16\right)} {y} \hspace{2em} x( -3 )= 2" title="{\left(t + 5\right)} {\left(t - 5\right)} = -{y'} {\left(t - 1\right)} e^{t} - {\left(t^{2} + 16\right)} {y} \hspace{2em} x( -3 )= 2" data-latex="{\left(t + 5\right)} {\left(t - 5\right)} = -{y'} {\left(t - 1\right)} e^{t} - {\left(t^{2} + 16\right)} {y} \hspace{2em} x( -3 )= 2"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%7B%5Cleft(t%20+%205%5Cright)%7D%20%7B%5Cleft(t%20-%205%5Cright)%7D%20=%20-%7By'%7D%20%7B%5Cleft(t%20-%201%5Cright)%7D%20e%5E%7Bt%7D%20-%20%7B%5Cleft(t%5E%7B2%7D%20+%2016%5Cright)%7D%20%7By%7D%20%5Chspace%7B2em%7D%20x(%20-3%20)=%202" alt="{\left(t + 5\right)} {\left(t - 5\right)} = -{y'} {\left(t - 1\right)} e^{t} - {\left(t^{2} + 16\right)} {y} \hspace{2em} x( -3 )= 2" title="{\left(t + 5\right)} {\left(t - 5\right)} = -{y'} {\left(t - 1\right)} e^{t} - {\left(t^{2} + 16\right)} {y} \hspace{2em} x( -3 )= 2" data-latex="{\left(t + 5\right)} {\left(t - 5\right)} = -{y'} {\left(t - 1\right)} e^{t} - {\left(t^{2} + 16\right)} {y} \hspace{2em} x( -3 )= 2"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-\infty,1)" alt="(-\infty,1)" title="(-\infty,1)" data-latex="(-\infty,1)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-%5Cinfty,1)" alt="(-\infty,1)" title="(-\infty,1)" data-latex="(-\infty,1)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-3714" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 3714"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-{y'} {\left(t + 1\right)} {\left(t - 6\right)} - {y} e^{\left(3 \, t\right)} = t + 6 \hspace{2em} x( 3 )= 10" alt="-{y'} {\left(t + 1\right)} {\left(t - 6\right)} - {y} e^{\left(3 \, t\right)} = t + 6 \hspace{2em} x( 3 )= 10" title="-{y'} {\left(t + 1\right)} {\left(t - 6\right)} - {y} e^{\left(3 \, t\right)} = t + 6 \hspace{2em} x( 3 )= 10" data-latex="-{y'} {\left(t + 1\right)} {\left(t - 6\right)} - {y} e^{\left(3 \, t\right)} = t + 6 \hspace{2em} x( 3 )= 10"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-%7By'%7D%20%7B%5Cleft(t%20+%201%5Cright)%7D%20%7B%5Cleft(t%20-%206%5Cright)%7D%20-%20%7By%7D%20e%5E%7B%5Cleft(3%20%5C,%20t%5Cright)%7D%20=%20t%20+%206%20%5Chspace%7B2em%7D%20x(%203%20)=%2010" alt="-{y'} {\left(t + 1\right)} {\left(t - 6\right)} - {y} e^{\left(3 \, t\right)} = t + 6 \hspace{2em} x( 3 )= 10" title="-{y'} {\left(t + 1\right)} {\left(t - 6\right)} - {y} e^{\left(3 \, t\right)} = t + 6 \hspace{2em} x( 3 )= 10" data-latex="-{y'} {\left(t + 1\right)} {\left(t - 6\right)} - {y} e^{\left(3 \, t\right)} = t + 6 \hspace{2em} x( 3 )= 10"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-1,6)" alt="(-1,6)" title="(-1,6)" data-latex="(-1,6)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-1,6)" alt="(-1,6)" title="(-1,6)" data-latex="(-1,6)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-2893" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 2893"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{\left(t^{2} + 16\right)} {y'} = -{y} {\left(t + 6\right)} {\left(t - 5\right)} - {\left(t - 1\right)} e^{t} \hspace{2em} x( 5 )= -1" alt="{\left(t^{2} + 16\right)} {y'} = -{y} {\left(t + 6\right)} {\left(t - 5\right)} - {\left(t - 1\right)} e^{t} \hspace{2em} x( 5 )= -1" title="{\left(t^{2} + 16\right)} {y'} = -{y} {\left(t + 6\right)} {\left(t - 5\right)} - {\left(t - 1\right)} e^{t} \hspace{2em} x( 5 )= -1" data-latex="{\left(t^{2} + 16\right)} {y'} = -{y} {\left(t + 6\right)} {\left(t - 5\right)} - {\left(t - 1\right)} e^{t} \hspace{2em} x( 5 )= -1"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%7B%5Cleft(t%5E%7B2%7D%20+%2016%5Cright)%7D%20%7By'%7D%20=%20-%7By%7D%20%7B%5Cleft(t%20+%206%5Cright)%7D%20%7B%5Cleft(t%20-%205%5Cright)%7D%20-%20%7B%5Cleft(t%20-%201%5Cright)%7D%20e%5E%7Bt%7D%20%5Chspace%7B2em%7D%20x(%205%20)=%20-1" alt="{\left(t^{2} + 16\right)} {y'} = -{y} {\left(t + 6\right)} {\left(t - 5\right)} - {\left(t - 1\right)} e^{t} \hspace{2em} x( 5 )= -1" title="{\left(t^{2} + 16\right)} {y'} = -{y} {\left(t + 6\right)} {\left(t - 5\right)} - {\left(t - 1\right)} e^{t} \hspace{2em} x( 5 )= -1" data-latex="{\left(t^{2} + 16\right)} {y'} = -{y} {\left(t + 6\right)} {\left(t - 5\right)} - {\left(t - 1\right)} e^{t} \hspace{2em} x( 5 )= -1"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-\infty,+\infty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-%5Cinfty,+%5Cinfty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-2009" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 2009"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-{y'} {\left(t + 2\right)} e^{t} = {\left(t^{2} + 25\right)} {y} + {\left(t + 4\right)} {\left(t - 6\right)} \hspace{2em} x( -5 )= 0" alt="-{y'} {\left(t + 2\right)} e^{t} = {\left(t^{2} + 25\right)} {y} + {\left(t + 4\right)} {\left(t - 6\right)} \hspace{2em} x( -5 )= 0" title="-{y'} {\left(t + 2\right)} e^{t} = {\left(t^{2} + 25\right)} {y} + {\left(t + 4\right)} {\left(t - 6\right)} \hspace{2em} x( -5 )= 0" data-latex="-{y'} {\left(t + 2\right)} e^{t} = {\left(t^{2} + 25\right)} {y} + {\left(t + 4\right)} {\left(t - 6\right)} \hspace{2em} x( -5 )= 0"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-%7By'%7D%20%7B%5Cleft(t%20+%202%5Cright)%7D%20e%5E%7Bt%7D%20=%20%7B%5Cleft(t%5E%7B2%7D%20+%2025%5Cright)%7D%20%7By%7D%20+%20%7B%5Cleft(t%20+%204%5Cright)%7D%20%7B%5Cleft(t%20-%206%5Cright)%7D%20%5Chspace%7B2em%7D%20x(%20-5%20)=%200" alt="-{y'} {\left(t + 2\right)} e^{t} = {\left(t^{2} + 25\right)} {y} + {\left(t + 4\right)} {\left(t - 6\right)} \hspace{2em} x( -5 )= 0" title="-{y'} {\left(t + 2\right)} e^{t} = {\left(t^{2} + 25\right)} {y} + {\left(t + 4\right)} {\left(t - 6\right)} \hspace{2em} x( -5 )= 0" data-latex="-{y'} {\left(t + 2\right)} e^{t} = {\left(t^{2} + 25\right)} {y} + {\left(t + 4\right)} {\left(t - 6\right)} \hspace{2em} x( -5 )= 0"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-\infty,-2)" alt="(-\infty,-2)" title="(-\infty,-2)" data-latex="(-\infty,-2)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-%5Cinfty,-2)" alt="(-\infty,-2)" title="(-\infty,-2)" data-latex="(-\infty,-2)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-4682" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 4682"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-{y} {\left(t + 2\right)} {\left(t - 6\right)} - t - 4 = {\left(t^{2} + 1\right)} {y'} \hspace{2em} x( -6 )= -6" alt="-{y} {\left(t + 2\right)} {\left(t - 6\right)} - t - 4 = {\left(t^{2} + 1\right)} {y'} \hspace{2em} x( -6 )= -6" title="-{y} {\left(t + 2\right)} {\left(t - 6\right)} - t - 4 = {\left(t^{2} + 1\right)} {y'} \hspace{2em} x( -6 )= -6" data-latex="-{y} {\left(t + 2\right)} {\left(t - 6\right)} - t - 4 = {\left(t^{2} + 1\right)} {y'} \hspace{2em} x( -6 )= -6"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-%7By%7D%20%7B%5Cleft(t%20+%202%5Cright)%7D%20%7B%5Cleft(t%20-%206%5Cright)%7D%20-%20t%20-%204%20=%20%7B%5Cleft(t%5E%7B2%7D%20+%201%5Cright)%7D%20%7By'%7D%20%5Chspace%7B2em%7D%20x(%20-6%20)=%20-6" alt="-{y} {\left(t + 2\right)} {\left(t - 6\right)} - t - 4 = {\left(t^{2} + 1\right)} {y'} \hspace{2em} x( -6 )= -6" title="-{y} {\left(t + 2\right)} {\left(t - 6\right)} - t - 4 = {\left(t^{2} + 1\right)} {y'} \hspace{2em} x( -6 )= -6" data-latex="-{y} {\left(t + 2\right)} {\left(t - 6\right)} - t - 4 = {\left(t^{2} + 1\right)} {y'} \hspace{2em} x( -6 )= -6"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-\infty,+\infty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-%5Cinfty,+%5Cinfty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-7557" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 7557"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-{\left(t^{2} + 4\right)} {y} - t + 6 = {y'} {\left(t + 6\right)} t \hspace{2em} x( -3 )= -7" alt="-{\left(t^{2} + 4\right)} {y} - t + 6 = {y'} {\left(t + 6\right)} t \hspace{2em} x( -3 )= -7" title="-{\left(t^{2} + 4\right)} {y} - t + 6 = {y'} {\left(t + 6\right)} t \hspace{2em} x( -3 )= -7" data-latex="-{\left(t^{2} + 4\right)} {y} - t + 6 = {y'} {\left(t + 6\right)} t \hspace{2em} x( -3 )= -7"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-%7B%5Cleft(t%5E%7B2%7D%20+%204%5Cright)%7D%20%7By%7D%20-%20t%20+%206%20=%20%7By'%7D%20%7B%5Cleft(t%20+%206%5Cright)%7D%20t%20%5Chspace%7B2em%7D%20x(%20-3%20)=%20-7" alt="-{\left(t^{2} + 4\right)} {y} - t + 6 = {y'} {\left(t + 6\right)} t \hspace{2em} x( -3 )= -7" title="-{\left(t^{2} + 4\right)} {y} - t + 6 = {y'} {\left(t + 6\right)} t \hspace{2em} x( -3 )= -7" data-latex="-{\left(t^{2} + 4\right)} {y} - t + 6 = {y'} {\left(t + 6\right)} t \hspace{2em} x( -3 )= -7"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-6,0)" alt="(-6,0)" title="(-6,0)" data-latex="(-6,0)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-6,0)" alt="(-6,0)" title="(-6,0)" data-latex="(-6,0)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-3311" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 3311"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-{y} {\left(t + 4\right)} e^{t} - {y'} e^{\left(4 \, t\right)} = {\left(t - 2\right)} {\left(t - 6\right)} \hspace{2em} x( -3 )= 4" alt="-{y} {\left(t + 4\right)} e^{t} - {y'} e^{\left(4 \, t\right)} = {\left(t - 2\right)} {\left(t - 6\right)} \hspace{2em} x( -3 )= 4" title="-{y} {\left(t + 4\right)} e^{t} - {y'} e^{\left(4 \, t\right)} = {\left(t - 2\right)} {\left(t - 6\right)} \hspace{2em} x( -3 )= 4" data-latex="-{y} {\left(t + 4\right)} e^{t} - {y'} e^{\left(4 \, t\right)} = {\left(t - 2\right)} {\left(t - 6\right)} \hspace{2em} x( -3 )= 4"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-%7By%7D%20%7B%5Cleft(t%20+%204%5Cright)%7D%20e%5E%7Bt%7D%20-%20%7By'%7D%20e%5E%7B%5Cleft(4%20%5C,%20t%5Cright)%7D%20=%20%7B%5Cleft(t%20-%202%5Cright)%7D%20%7B%5Cleft(t%20-%206%5Cright)%7D%20%5Chspace%7B2em%7D%20x(%20-3%20)=%204" alt="-{y} {\left(t + 4\right)} e^{t} - {y'} e^{\left(4 \, t\right)} = {\left(t - 2\right)} {\left(t - 6\right)} \hspace{2em} x( -3 )= 4" title="-{y} {\left(t + 4\right)} e^{t} - {y'} e^{\left(4 \, t\right)} = {\left(t - 2\right)} {\left(t - 6\right)} \hspace{2em} x( -3 )= 4" data-latex="-{y} {\left(t + 4\right)} e^{t} - {y'} e^{\left(4 \, t\right)} = {\left(t - 2\right)} {\left(t - 6\right)} \hspace{2em} x( -3 )= 4"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-\infty,+\infty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-%5Cinfty,+%5Cinfty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-0542" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 0542"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?0 = -{y'} {\left(t - 6\right)} e^{t} - {\left(t + 6\right)} {\left(t + 1\right)} - {y} e^{\left(-4 \, t\right)} \hspace{2em} x( 9 )= 2" alt="0 = -{y'} {\left(t - 6\right)} e^{t} - {\left(t + 6\right)} {\left(t + 1\right)} - {y} e^{\left(-4 \, t\right)} \hspace{2em} x( 9 )= 2" title="0 = -{y'} {\left(t - 6\right)} e^{t} - {\left(t + 6\right)} {\left(t + 1\right)} - {y} e^{\left(-4 \, t\right)} \hspace{2em} x( 9 )= 2" data-latex="0 = -{y'} {\left(t - 6\right)} e^{t} - {\left(t + 6\right)} {\left(t + 1\right)} - {y} e^{\left(-4 \, t\right)} \hspace{2em} x( 9 )= 2"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?0%20=%20-%7By'%7D%20%7B%5Cleft(t%20-%206%5Cright)%7D%20e%5E%7Bt%7D%20-%20%7B%5Cleft(t%20+%206%5Cright)%7D%20%7B%5Cleft(t%20+%201%5Cright)%7D%20-%20%7By%7D%20e%5E%7B%5Cleft(-4%20%5C,%20t%5Cright)%7D%20%5Chspace%7B2em%7D%20x(%209%20)=%202" alt="0 = -{y'} {\left(t - 6\right)} e^{t} - {\left(t + 6\right)} {\left(t + 1\right)} - {y} e^{\left(-4 \, t\right)} \hspace{2em} x( 9 )= 2" title="0 = -{y'} {\left(t - 6\right)} e^{t} - {\left(t + 6\right)} {\left(t + 1\right)} - {y} e^{\left(-4 \, t\right)} \hspace{2em} x( 9 )= 2" data-latex="0 = -{y'} {\left(t - 6\right)} e^{t} - {\left(t + 6\right)} {\left(t + 1\right)} - {y} e^{\left(-4 \, t\right)} \hspace{2em} x( 9 )= 2"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(6,+\infty)" alt="(6,+\infty)" title="(6,+\infty)" data-latex="(6,+\infty)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(6,+%5Cinfty)" alt="(6,+\infty)" title="(6,+\infty)" data-latex="(6,+\infty)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-9483" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 9483"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y'} {\left(t + 4\right)} {\left(t - 1\right)} + {\left(t^{2} + 9\right)} {y} = -{\left(t - 6\right)} e^{t} \hspace{2em} x( -2 )= -7" alt="{y'} {\left(t + 4\right)} {\left(t - 1\right)} + {\left(t^{2} + 9\right)} {y} = -{\left(t - 6\right)} e^{t} \hspace{2em} x( -2 )= -7" title="{y'} {\left(t + 4\right)} {\left(t - 1\right)} + {\left(t^{2} + 9\right)} {y} = -{\left(t - 6\right)} e^{t} \hspace{2em} x( -2 )= -7" data-latex="{y'} {\left(t + 4\right)} {\left(t - 1\right)} + {\left(t^{2} + 9\right)} {y} = -{\left(t - 6\right)} e^{t} \hspace{2em} x( -2 )= -7"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%7By'%7D%20%7B%5Cleft(t%20+%204%5Cright)%7D%20%7B%5Cleft(t%20-%201%5Cright)%7D%20+%20%7B%5Cleft(t%5E%7B2%7D%20+%209%5Cright)%7D%20%7By%7D%20=%20-%7B%5Cleft(t%20-%206%5Cright)%7D%20e%5E%7Bt%7D%20%5Chspace%7B2em%7D%20x(%20-2%20)=%20-7" alt="{y'} {\left(t + 4\right)} {\left(t - 1\right)} + {\left(t^{2} + 9\right)} {y} = -{\left(t - 6\right)} e^{t} \hspace{2em} x( -2 )= -7" title="{y'} {\left(t + 4\right)} {\left(t - 1\right)} + {\left(t^{2} + 9\right)} {y} = -{\left(t - 6\right)} e^{t} \hspace{2em} x( -2 )= -7" data-latex="{y'} {\left(t + 4\right)} {\left(t - 1\right)} + {\left(t^{2} + 9\right)} {y} = -{\left(t - 6\right)} e^{t} \hspace{2em} x( -2 )= -7"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-4,1)" alt="(-4,1)" title="(-4,1)" data-latex="(-4,1)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-4,1)" alt="(-4,1)" title="(-4,1)" data-latex="(-4,1)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-0414" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 0414"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-{\left(t^{2} + 9\right)} {y'} = {y} {\left(t - 5\right)} e^{t} + {\left(t + 5\right)} {\left(t + 1\right)} \hspace{2em} x( 3 )= -4" alt="-{\left(t^{2} + 9\right)} {y'} = {y} {\left(t - 5\right)} e^{t} + {\left(t + 5\right)} {\left(t + 1\right)} \hspace{2em} x( 3 )= -4" title="-{\left(t^{2} + 9\right)} {y'} = {y} {\left(t - 5\right)} e^{t} + {\left(t + 5\right)} {\left(t + 1\right)} \hspace{2em} x( 3 )= -4" data-latex="-{\left(t^{2} + 9\right)} {y'} = {y} {\left(t - 5\right)} e^{t} + {\left(t + 5\right)} {\left(t + 1\right)} \hspace{2em} x( 3 )= -4"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-%7B%5Cleft(t%5E%7B2%7D%20+%209%5Cright)%7D%20%7By'%7D%20=%20%7By%7D%20%7B%5Cleft(t%20-%205%5Cright)%7D%20e%5E%7Bt%7D%20+%20%7B%5Cleft(t%20+%205%5Cright)%7D%20%7B%5Cleft(t%20+%201%5Cright)%7D%20%5Chspace%7B2em%7D%20x(%203%20)=%20-4" alt="-{\left(t^{2} + 9\right)} {y'} = {y} {\left(t - 5\right)} e^{t} + {\left(t + 5\right)} {\left(t + 1\right)} \hspace{2em} x( 3 )= -4" title="-{\left(t^{2} + 9\right)} {y'} = {y} {\left(t - 5\right)} e^{t} + {\left(t + 5\right)} {\left(t + 1\right)} \hspace{2em} x( 3 )= -4" data-latex="-{\left(t^{2} + 9\right)} {y'} = {y} {\left(t - 5\right)} e^{t} + {\left(t + 5\right)} {\left(t + 1\right)} \hspace{2em} x( 3 )= -4"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-\infty,+\infty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-%5Cinfty,+%5Cinfty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-2409" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 2409"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?0 = {y'} {\left(t + 5\right)} e^{t} + {\left(t^{2} + 16\right)} {y} + {\left(t - 1\right)} {\left(t - 6\right)} \hspace{2em} x( -8 )= -3" alt="0 = {y'} {\left(t + 5\right)} e^{t} + {\left(t^{2} + 16\right)} {y} + {\left(t - 1\right)} {\left(t - 6\right)} \hspace{2em} x( -8 )= -3" title="0 = {y'} {\left(t + 5\right)} e^{t} + {\left(t^{2} + 16\right)} {y} + {\left(t - 1\right)} {\left(t - 6\right)} \hspace{2em} x( -8 )= -3" data-latex="0 = {y'} {\left(t + 5\right)} e^{t} + {\left(t^{2} + 16\right)} {y} + {\left(t - 1\right)} {\left(t - 6\right)} \hspace{2em} x( -8 )= -3"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?0%20=%20%7By'%7D%20%7B%5Cleft(t%20+%205%5Cright)%7D%20e%5E%7Bt%7D%20+%20%7B%5Cleft(t%5E%7B2%7D%20+%2016%5Cright)%7D%20%7By%7D%20+%20%7B%5Cleft(t%20-%201%5Cright)%7D%20%7B%5Cleft(t%20-%206%5Cright)%7D%20%5Chspace%7B2em%7D%20x(%20-8%20)=%20-3" alt="0 = {y'} {\left(t + 5\right)} e^{t} + {\left(t^{2} + 16\right)} {y} + {\left(t - 1\right)} {\left(t - 6\right)} \hspace{2em} x( -8 )= -3" title="0 = {y'} {\left(t + 5\right)} e^{t} + {\left(t^{2} + 16\right)} {y} + {\left(t - 1\right)} {\left(t - 6\right)} \hspace{2em} x( -8 )= -3" data-latex="0 = {y'} {\left(t + 5\right)} e^{t} + {\left(t^{2} + 16\right)} {y} + {\left(t - 1\right)} {\left(t - 6\right)} \hspace{2em} x( -8 )= -3"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-\infty,-5)" alt="(-\infty,-5)" title="(-\infty,-5)" data-latex="(-\infty,-5)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-%5Cinfty,-5)" alt="(-\infty,-5)" title="(-\infty,-5)" data-latex="(-\infty,-5)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-0023" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 0023"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y'} e^{\left(-5 \, t\right)} = -{\left(t + 2\right)} {\left(t - 6\right)} {y} - t - 6 \hspace{2em} x( -1 )= 2" alt="{y'} e^{\left(-5 \, t\right)} = -{\left(t + 2\right)} {\left(t - 6\right)} {y} - t - 6 \hspace{2em} x( -1 )= 2" title="{y'} e^{\left(-5 \, t\right)} = -{\left(t + 2\right)} {\left(t - 6\right)} {y} - t - 6 \hspace{2em} x( -1 )= 2" data-latex="{y'} e^{\left(-5 \, t\right)} = -{\left(t + 2\right)} {\left(t - 6\right)} {y} - t - 6 \hspace{2em} x( -1 )= 2"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%7By'%7D%20e%5E%7B%5Cleft(-5%20%5C,%20t%5Cright)%7D%20=%20-%7B%5Cleft(t%20+%202%5Cright)%7D%20%7B%5Cleft(t%20-%206%5Cright)%7D%20%7By%7D%20-%20t%20-%206%20%5Chspace%7B2em%7D%20x(%20-1%20)=%202" alt="{y'} e^{\left(-5 \, t\right)} = -{\left(t + 2\right)} {\left(t - 6\right)} {y} - t - 6 \hspace{2em} x( -1 )= 2" title="{y'} e^{\left(-5 \, t\right)} = -{\left(t + 2\right)} {\left(t - 6\right)} {y} - t - 6 \hspace{2em} x( -1 )= 2" data-latex="{y'} e^{\left(-5 \, t\right)} = -{\left(t + 2\right)} {\left(t - 6\right)} {y} - t - 6 \hspace{2em} x( -1 )= 2"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-\infty,+\infty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-%5Cinfty,+%5Cinfty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-4645" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 4645"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-{\left(t - 1\right)} {\left(t - 5\right)} {y} - {y'} e^{\left(-3 \, t\right)} = {\left(t + 6\right)} e^{t} \hspace{2em} x( 5 )= -4" alt="-{\left(t - 1\right)} {\left(t - 5\right)} {y} - {y'} e^{\left(-3 \, t\right)} = {\left(t + 6\right)} e^{t} \hspace{2em} x( 5 )= -4" title="-{\left(t - 1\right)} {\left(t - 5\right)} {y} - {y'} e^{\left(-3 \, t\right)} = {\left(t + 6\right)} e^{t} \hspace{2em} x( 5 )= -4" data-latex="-{\left(t - 1\right)} {\left(t - 5\right)} {y} - {y'} e^{\left(-3 \, t\right)} = {\left(t + 6\right)} e^{t} \hspace{2em} x( 5 )= -4"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-%7B%5Cleft(t%20-%201%5Cright)%7D%20%7B%5Cleft(t%20-%205%5Cright)%7D%20%7By%7D%20-%20%7By'%7D%20e%5E%7B%5Cleft(-3%20%5C,%20t%5Cright)%7D%20=%20%7B%5Cleft(t%20+%206%5Cright)%7D%20e%5E%7Bt%7D%20%5Chspace%7B2em%7D%20x(%205%20)=%20-4" alt="-{\left(t - 1\right)} {\left(t - 5\right)} {y} - {y'} e^{\left(-3 \, t\right)} = {\left(t + 6\right)} e^{t} \hspace{2em} x( 5 )= -4" title="-{\left(t - 1\right)} {\left(t - 5\right)} {y} - {y'} e^{\left(-3 \, t\right)} = {\left(t + 6\right)} e^{t} \hspace{2em} x( 5 )= -4" data-latex="-{\left(t - 1\right)} {\left(t - 5\right)} {y} - {y'} e^{\left(-3 \, t\right)} = {\left(t + 6\right)} e^{t} \hspace{2em} x( 5 )= -4"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-\infty,+\infty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-%5Cinfty,+%5Cinfty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-3606" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 3606"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{\left(t + 6\right)} {\left(t + 2\right)} = -{\left(t - 6\right)} {y} e^{t} - {\left(t^{2} + 1\right)} {y'} \hspace{2em} x( -4 )= -2" alt="{\left(t + 6\right)} {\left(t + 2\right)} = -{\left(t - 6\right)} {y} e^{t} - {\left(t^{2} + 1\right)} {y'} \hspace{2em} x( -4 )= -2" title="{\left(t + 6\right)} {\left(t + 2\right)} = -{\left(t - 6\right)} {y} e^{t} - {\left(t^{2} + 1\right)} {y'} \hspace{2em} x( -4 )= -2" data-latex="{\left(t + 6\right)} {\left(t + 2\right)} = -{\left(t - 6\right)} {y} e^{t} - {\left(t^{2} + 1\right)} {y'} \hspace{2em} x( -4 )= -2"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%7B%5Cleft(t%20+%206%5Cright)%7D%20%7B%5Cleft(t%20+%202%5Cright)%7D%20=%20-%7B%5Cleft(t%20-%206%5Cright)%7D%20%7By%7D%20e%5E%7Bt%7D%20-%20%7B%5Cleft(t%5E%7B2%7D%20+%201%5Cright)%7D%20%7By'%7D%20%5Chspace%7B2em%7D%20x(%20-4%20)=%20-2" alt="{\left(t + 6\right)} {\left(t + 2\right)} = -{\left(t - 6\right)} {y} e^{t} - {\left(t^{2} + 1\right)} {y'} \hspace{2em} x( -4 )= -2" title="{\left(t + 6\right)} {\left(t + 2\right)} = -{\left(t - 6\right)} {y} e^{t} - {\left(t^{2} + 1\right)} {y'} \hspace{2em} x( -4 )= -2" data-latex="{\left(t + 6\right)} {\left(t + 2\right)} = -{\left(t - 6\right)} {y} e^{t} - {\left(t^{2} + 1\right)} {y'} \hspace{2em} x( -4 )= -2"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-\infty,+\infty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-%5Cinfty,+%5Cinfty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-6035" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 6035"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-{\left(t^{2} + 25\right)} {y'} - {y} {\left(t - 5\right)} - {\left(t + 5\right)} t = 0 \hspace{2em} x( -5 )= 6" alt="-{\left(t^{2} + 25\right)} {y'} - {y} {\left(t - 5\right)} - {\left(t + 5\right)} t = 0 \hspace{2em} x( -5 )= 6" title="-{\left(t^{2} + 25\right)} {y'} - {y} {\left(t - 5\right)} - {\left(t + 5\right)} t = 0 \hspace{2em} x( -5 )= 6" data-latex="-{\left(t^{2} + 25\right)} {y'} - {y} {\left(t - 5\right)} - {\left(t + 5\right)} t = 0 \hspace{2em} x( -5 )= 6"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-%7B%5Cleft(t%5E%7B2%7D%20+%2025%5Cright)%7D%20%7By'%7D%20-%20%7By%7D%20%7B%5Cleft(t%20-%205%5Cright)%7D%20-%20%7B%5Cleft(t%20+%205%5Cright)%7D%20t%20=%200%20%5Chspace%7B2em%7D%20x(%20-5%20)=%206" alt="-{\left(t^{2} + 25\right)} {y'} - {y} {\left(t - 5\right)} - {\left(t + 5\right)} t = 0 \hspace{2em} x( -5 )= 6" title="-{\left(t^{2} + 25\right)} {y'} - {y} {\left(t - 5\right)} - {\left(t + 5\right)} t = 0 \hspace{2em} x( -5 )= 6" data-latex="-{\left(t^{2} + 25\right)} {y'} - {y} {\left(t - 5\right)} - {\left(t + 5\right)} t = 0 \hspace{2em} x( -5 )= 6"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-\infty,+\infty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-%5Cinfty,+%5Cinfty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-6966" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 6966"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-{y'} {\left(t + 5\right)} {\left(t + 1\right)} - {y} e^{\left(3 \, t\right)} = {\left(t - 5\right)} e^{t} \hspace{2em} x( -4 )= -9" alt="-{y'} {\left(t + 5\right)} {\left(t + 1\right)} - {y} e^{\left(3 \, t\right)} = {\left(t - 5\right)} e^{t} \hspace{2em} x( -4 )= -9" title="-{y'} {\left(t + 5\right)} {\left(t + 1\right)} - {y} e^{\left(3 \, t\right)} = {\left(t - 5\right)} e^{t} \hspace{2em} x( -4 )= -9" data-latex="-{y'} {\left(t + 5\right)} {\left(t + 1\right)} - {y} e^{\left(3 \, t\right)} = {\left(t - 5\right)} e^{t} \hspace{2em} x( -4 )= -9"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-%7By'%7D%20%7B%5Cleft(t%20+%205%5Cright)%7D%20%7B%5Cleft(t%20+%201%5Cright)%7D%20-%20%7By%7D%20e%5E%7B%5Cleft(3%20%5C,%20t%5Cright)%7D%20=%20%7B%5Cleft(t%20-%205%5Cright)%7D%20e%5E%7Bt%7D%20%5Chspace%7B2em%7D%20x(%20-4%20)=%20-9" alt="-{y'} {\left(t + 5\right)} {\left(t + 1\right)} - {y} e^{\left(3 \, t\right)} = {\left(t - 5\right)} e^{t} \hspace{2em} x( -4 )= -9" title="-{y'} {\left(t + 5\right)} {\left(t + 1\right)} - {y} e^{\left(3 \, t\right)} = {\left(t - 5\right)} e^{t} \hspace{2em} x( -4 )= -9" data-latex="-{y'} {\left(t + 5\right)} {\left(t + 1\right)} - {y} e^{\left(3 \, t\right)} = {\left(t - 5\right)} e^{t} \hspace{2em} x( -4 )= -9"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-5,-1)" alt="(-5,-1)" title="(-5,-1)" data-latex="(-5,-1)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-5,-1)" alt="(-5,-1)" title="(-5,-1)" data-latex="(-5,-1)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-3000" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 3000"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?0 = -{\left(t + 6\right)} {\left(t - 5\right)} {y'} - {\left(t^{2} + 4\right)} {y} - t \hspace{2em} x( 0 )= 9" alt="0 = -{\left(t + 6\right)} {\left(t - 5\right)} {y'} - {\left(t^{2} + 4\right)} {y} - t \hspace{2em} x( 0 )= 9" title="0 = -{\left(t + 6\right)} {\left(t - 5\right)} {y'} - {\left(t^{2} + 4\right)} {y} - t \hspace{2em} x( 0 )= 9" data-latex="0 = -{\left(t + 6\right)} {\left(t - 5\right)} {y'} - {\left(t^{2} + 4\right)} {y} - t \hspace{2em} x( 0 )= 9"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?0%20=%20-%7B%5Cleft(t%20+%206%5Cright)%7D%20%7B%5Cleft(t%20-%205%5Cright)%7D%20%7By'%7D%20-%20%7B%5Cleft(t%5E%7B2%7D%20+%204%5Cright)%7D%20%7By%7D%20-%20t%20%5Chspace%7B2em%7D%20x(%200%20)=%209" alt="0 = -{\left(t + 6\right)} {\left(t - 5\right)} {y'} - {\left(t^{2} + 4\right)} {y} - t \hspace{2em} x( 0 )= 9" title="0 = -{\left(t + 6\right)} {\left(t - 5\right)} {y'} - {\left(t^{2} + 4\right)} {y} - t \hspace{2em} x( 0 )= 9" data-latex="0 = -{\left(t + 6\right)} {\left(t - 5\right)} {y'} - {\left(t^{2} + 4\right)} {y} - t \hspace{2em} x( 0 )= 9"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-6,5)" alt="(-6,5)" title="(-6,5)" data-latex="(-6,5)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-6,5)" alt="(-6,5)" title="(-6,5)" data-latex="(-6,5)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-5261" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 5261"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y} t e^{t} + {\left(t^{2} + 1\right)} {y'} + {\left(t + 6\right)} {\left(t - 5\right)} = 0 \hspace{2em} x( -6 )= -3" alt="{y} t e^{t} + {\left(t^{2} + 1\right)} {y'} + {\left(t + 6\right)} {\left(t - 5\right)} = 0 \hspace{2em} x( -6 )= -3" title="{y} t e^{t} + {\left(t^{2} + 1\right)} {y'} + {\left(t + 6\right)} {\left(t - 5\right)} = 0 \hspace{2em} x( -6 )= -3" data-latex="{y} t e^{t} + {\left(t^{2} + 1\right)} {y'} + {\left(t + 6\right)} {\left(t - 5\right)} = 0 \hspace{2em} x( -6 )= -3"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%7By%7D%20t%20e%5E%7Bt%7D%20+%20%7B%5Cleft(t%5E%7B2%7D%20+%201%5Cright)%7D%20%7By'%7D%20+%20%7B%5Cleft(t%20+%206%5Cright)%7D%20%7B%5Cleft(t%20-%205%5Cright)%7D%20=%200%20%5Chspace%7B2em%7D%20x(%20-6%20)=%20-3" alt="{y} t e^{t} + {\left(t^{2} + 1\right)} {y'} + {\left(t + 6\right)} {\left(t - 5\right)} = 0 \hspace{2em} x( -6 )= -3" title="{y} t e^{t} + {\left(t^{2} + 1\right)} {y'} + {\left(t + 6\right)} {\left(t - 5\right)} = 0 \hspace{2em} x( -6 )= -3" data-latex="{y} t e^{t} + {\left(t^{2} + 1\right)} {y'} + {\left(t + 6\right)} {\left(t - 5\right)} = 0 \hspace{2em} x( -6 )= -3"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-\infty,+\infty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-%5Cinfty,+%5Cinfty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-1981" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 1981"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{\left(t + 4\right)} {\left(t - 6\right)} {y'} + {y} e^{\left(-t\right)} + t e^{t} = 0 \hspace{2em} x( 2 )= 10" alt="{\left(t + 4\right)} {\left(t - 6\right)} {y'} + {y} e^{\left(-t\right)} + t e^{t} = 0 \hspace{2em} x( 2 )= 10" title="{\left(t + 4\right)} {\left(t - 6\right)} {y'} + {y} e^{\left(-t\right)} + t e^{t} = 0 \hspace{2em} x( 2 )= 10" data-latex="{\left(t + 4\right)} {\left(t - 6\right)} {y'} + {y} e^{\left(-t\right)} + t e^{t} = 0 \hspace{2em} x( 2 )= 10"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%7B%5Cleft(t%20+%204%5Cright)%7D%20%7B%5Cleft(t%20-%206%5Cright)%7D%20%7By'%7D%20+%20%7By%7D%20e%5E%7B%5Cleft(-t%5Cright)%7D%20+%20t%20e%5E%7Bt%7D%20=%200%20%5Chspace%7B2em%7D%20x(%202%20)=%2010" alt="{\left(t + 4\right)} {\left(t - 6\right)} {y'} + {y} e^{\left(-t\right)} + t e^{t} = 0 \hspace{2em} x( 2 )= 10" title="{\left(t + 4\right)} {\left(t - 6\right)} {y'} + {y} e^{\left(-t\right)} + t e^{t} = 0 \hspace{2em} x( 2 )= 10" data-latex="{\left(t + 4\right)} {\left(t - 6\right)} {y'} + {y} e^{\left(-t\right)} + t e^{t} = 0 \hspace{2em} x( 2 )= 10"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-4,6)" alt="(-4,6)" title="(-4,6)" data-latex="(-4,6)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-4,6)" alt="(-4,6)" title="(-4,6)" data-latex="(-4,6)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-0035" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 0035"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y} {\left(t + 1\right)} {\left(t - 5\right)} + {y'} {\left(t + 4\right)} e^{t} = -t^{2} - 4 \hspace{2em} x( -8 )= -1" alt="{y} {\left(t + 1\right)} {\left(t - 5\right)} + {y'} {\left(t + 4\right)} e^{t} = -t^{2} - 4 \hspace{2em} x( -8 )= -1" title="{y} {\left(t + 1\right)} {\left(t - 5\right)} + {y'} {\left(t + 4\right)} e^{t} = -t^{2} - 4 \hspace{2em} x( -8 )= -1" data-latex="{y} {\left(t + 1\right)} {\left(t - 5\right)} + {y'} {\left(t + 4\right)} e^{t} = -t^{2} - 4 \hspace{2em} x( -8 )= -1"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%7By%7D%20%7B%5Cleft(t%20+%201%5Cright)%7D%20%7B%5Cleft(t%20-%205%5Cright)%7D%20+%20%7By'%7D%20%7B%5Cleft(t%20+%204%5Cright)%7D%20e%5E%7Bt%7D%20=%20-t%5E%7B2%7D%20-%204%20%5Chspace%7B2em%7D%20x(%20-8%20)=%20-1" alt="{y} {\left(t + 1\right)} {\left(t - 5\right)} + {y'} {\left(t + 4\right)} e^{t} = -t^{2} - 4 \hspace{2em} x( -8 )= -1" title="{y} {\left(t + 1\right)} {\left(t - 5\right)} + {y'} {\left(t + 4\right)} e^{t} = -t^{2} - 4 \hspace{2em} x( -8 )= -1" data-latex="{y} {\left(t + 1\right)} {\left(t - 5\right)} + {y'} {\left(t + 4\right)} e^{t} = -t^{2} - 4 \hspace{2em} x( -8 )= -1"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-\infty,-4)" alt="(-\infty,-4)" title="(-\infty,-4)" data-latex="(-\infty,-4)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-%5Cinfty,-4)" alt="(-\infty,-4)" title="(-\infty,-4)" data-latex="(-\infty,-4)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-6043" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 6043"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-{\left(t + 1\right)} {y} e^{t} - {y'} e^{\left(2 \, t\right)} = {\left(t + 6\right)} {\left(t - 6\right)} \hspace{2em} x( 0 )= -2" alt="-{\left(t + 1\right)} {y} e^{t} - {y'} e^{\left(2 \, t\right)} = {\left(t + 6\right)} {\left(t - 6\right)} \hspace{2em} x( 0 )= -2" title="-{\left(t + 1\right)} {y} e^{t} - {y'} e^{\left(2 \, t\right)} = {\left(t + 6\right)} {\left(t - 6\right)} \hspace{2em} x( 0 )= -2" data-latex="-{\left(t + 1\right)} {y} e^{t} - {y'} e^{\left(2 \, t\right)} = {\left(t + 6\right)} {\left(t - 6\right)} \hspace{2em} x( 0 )= -2"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-%7B%5Cleft(t%20+%201%5Cright)%7D%20%7By%7D%20e%5E%7Bt%7D%20-%20%7By'%7D%20e%5E%7B%5Cleft(2%20%5C,%20t%5Cright)%7D%20=%20%7B%5Cleft(t%20+%206%5Cright)%7D%20%7B%5Cleft(t%20-%206%5Cright)%7D%20%5Chspace%7B2em%7D%20x(%200%20)=%20-2" alt="-{\left(t + 1\right)} {y} e^{t} - {y'} e^{\left(2 \, t\right)} = {\left(t + 6\right)} {\left(t - 6\right)} \hspace{2em} x( 0 )= -2" title="-{\left(t + 1\right)} {y} e^{t} - {y'} e^{\left(2 \, t\right)} = {\left(t + 6\right)} {\left(t - 6\right)} \hspace{2em} x( 0 )= -2" data-latex="-{\left(t + 1\right)} {y} e^{t} - {y'} e^{\left(2 \, t\right)} = {\left(t + 6\right)} {\left(t - 6\right)} \hspace{2em} x( 0 )= -2"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-\infty,+\infty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-%5Cinfty,+%5Cinfty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-0684" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 0684"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y} {\left(t + 2\right)} e^{t} + {\left(t + 6\right)} {\left(t - 6\right)} = -{\left(t^{2} + 16\right)} {y'} \hspace{2em} x( -6 )= 1" alt="{y} {\left(t + 2\right)} e^{t} + {\left(t + 6\right)} {\left(t - 6\right)} = -{\left(t^{2} + 16\right)} {y'} \hspace{2em} x( -6 )= 1" title="{y} {\left(t + 2\right)} e^{t} + {\left(t + 6\right)} {\left(t - 6\right)} = -{\left(t^{2} + 16\right)} {y'} \hspace{2em} x( -6 )= 1" data-latex="{y} {\left(t + 2\right)} e^{t} + {\left(t + 6\right)} {\left(t - 6\right)} = -{\left(t^{2} + 16\right)} {y'} \hspace{2em} x( -6 )= 1"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%7By%7D%20%7B%5Cleft(t%20+%202%5Cright)%7D%20e%5E%7Bt%7D%20+%20%7B%5Cleft(t%20+%206%5Cright)%7D%20%7B%5Cleft(t%20-%206%5Cright)%7D%20=%20-%7B%5Cleft(t%5E%7B2%7D%20+%2016%5Cright)%7D%20%7By'%7D%20%5Chspace%7B2em%7D%20x(%20-6%20)=%201" alt="{y} {\left(t + 2\right)} e^{t} + {\left(t + 6\right)} {\left(t - 6\right)} = -{\left(t^{2} + 16\right)} {y'} \hspace{2em} x( -6 )= 1" title="{y} {\left(t + 2\right)} e^{t} + {\left(t + 6\right)} {\left(t - 6\right)} = -{\left(t^{2} + 16\right)} {y'} \hspace{2em} x( -6 )= 1" data-latex="{y} {\left(t + 2\right)} e^{t} + {\left(t + 6\right)} {\left(t - 6\right)} = -{\left(t^{2} + 16\right)} {y'} \hspace{2em} x( -6 )= 1"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-\infty,+\infty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-%5Cinfty,+%5Cinfty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-4607" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 4607"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-{y} e^{\left(4 \, t\right)} - t + 1 = {y'} {\left(t + 6\right)} {\left(t - 6\right)} \hspace{2em} x( -4 )= -8" alt="-{y} e^{\left(4 \, t\right)} - t + 1 = {y'} {\left(t + 6\right)} {\left(t - 6\right)} \hspace{2em} x( -4 )= -8" title="-{y} e^{\left(4 \, t\right)} - t + 1 = {y'} {\left(t + 6\right)} {\left(t - 6\right)} \hspace{2em} x( -4 )= -8" data-latex="-{y} e^{\left(4 \, t\right)} - t + 1 = {y'} {\left(t + 6\right)} {\left(t - 6\right)} \hspace{2em} x( -4 )= -8"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-%7By%7D%20e%5E%7B%5Cleft(4%20%5C,%20t%5Cright)%7D%20-%20t%20+%201%20=%20%7By'%7D%20%7B%5Cleft(t%20+%206%5Cright)%7D%20%7B%5Cleft(t%20-%206%5Cright)%7D%20%5Chspace%7B2em%7D%20x(%20-4%20)=%20-8" alt="-{y} e^{\left(4 \, t\right)} - t + 1 = {y'} {\left(t + 6\right)} {\left(t - 6\right)} \hspace{2em} x( -4 )= -8" title="-{y} e^{\left(4 \, t\right)} - t + 1 = {y'} {\left(t + 6\right)} {\left(t - 6\right)} \hspace{2em} x( -4 )= -8" data-latex="-{y} e^{\left(4 \, t\right)} - t + 1 = {y'} {\left(t + 6\right)} {\left(t - 6\right)} \hspace{2em} x( -4 )= -8"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-6,6)" alt="(-6,6)" title="(-6,6)" data-latex="(-6,6)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-6,6)" alt="(-6,6)" title="(-6,6)" data-latex="(-6,6)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-5631" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 5631"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?0 = -{\left(t + 5\right)} {\left(t - 6\right)} {y'} - {\left(t - 1\right)} {y} e^{t} - t^{2} - 1 \hspace{2em} x( -3 )= -7" alt="0 = -{\left(t + 5\right)} {\left(t - 6\right)} {y'} - {\left(t - 1\right)} {y} e^{t} - t^{2} - 1 \hspace{2em} x( -3 )= -7" title="0 = -{\left(t + 5\right)} {\left(t - 6\right)} {y'} - {\left(t - 1\right)} {y} e^{t} - t^{2} - 1 \hspace{2em} x( -3 )= -7" data-latex="0 = -{\left(t + 5\right)} {\left(t - 6\right)} {y'} - {\left(t - 1\right)} {y} e^{t} - t^{2} - 1 \hspace{2em} x( -3 )= -7"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?0%20=%20-%7B%5Cleft(t%20+%205%5Cright)%7D%20%7B%5Cleft(t%20-%206%5Cright)%7D%20%7By'%7D%20-%20%7B%5Cleft(t%20-%201%5Cright)%7D%20%7By%7D%20e%5E%7Bt%7D%20-%20t%5E%7B2%7D%20-%201%20%5Chspace%7B2em%7D%20x(%20-3%20)=%20-7" alt="0 = -{\left(t + 5\right)} {\left(t - 6\right)} {y'} - {\left(t - 1\right)} {y} e^{t} - t^{2} - 1 \hspace{2em} x( -3 )= -7" title="0 = -{\left(t + 5\right)} {\left(t - 6\right)} {y'} - {\left(t - 1\right)} {y} e^{t} - t^{2} - 1 \hspace{2em} x( -3 )= -7" data-latex="0 = -{\left(t + 5\right)} {\left(t - 6\right)} {y'} - {\left(t - 1\right)} {y} e^{t} - t^{2} - 1 \hspace{2em} x( -3 )= -7"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-5,6)" alt="(-5,6)" title="(-5,6)" data-latex="(-5,6)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-5,6)" alt="(-5,6)" title="(-5,6)" data-latex="(-5,6)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-1948" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 1948"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{\left(t^{2} + 16\right)} {y'} = -{y} {\left(t - 1\right)} {\left(t - 6\right)} - t - 5 \hspace{2em} x( 4 )= -4" alt="{\left(t^{2} + 16\right)} {y'} = -{y} {\left(t - 1\right)} {\left(t - 6\right)} - t - 5 \hspace{2em} x( 4 )= -4" title="{\left(t^{2} + 16\right)} {y'} = -{y} {\left(t - 1\right)} {\left(t - 6\right)} - t - 5 \hspace{2em} x( 4 )= -4" data-latex="{\left(t^{2} + 16\right)} {y'} = -{y} {\left(t - 1\right)} {\left(t - 6\right)} - t - 5 \hspace{2em} x( 4 )= -4"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%7B%5Cleft(t%5E%7B2%7D%20+%2016%5Cright)%7D%20%7By'%7D%20=%20-%7By%7D%20%7B%5Cleft(t%20-%201%5Cright)%7D%20%7B%5Cleft(t%20-%206%5Cright)%7D%20-%20t%20-%205%20%5Chspace%7B2em%7D%20x(%204%20)=%20-4" alt="{\left(t^{2} + 16\right)} {y'} = -{y} {\left(t - 1\right)} {\left(t - 6\right)} - t - 5 \hspace{2em} x( 4 )= -4" title="{\left(t^{2} + 16\right)} {y'} = -{y} {\left(t - 1\right)} {\left(t - 6\right)} - t - 5 \hspace{2em} x( 4 )= -4" data-latex="{\left(t^{2} + 16\right)} {y'} = -{y} {\left(t - 1\right)} {\left(t - 6\right)} - t - 5 \hspace{2em} x( 4 )= -4"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-\infty,+\infty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-%5Cinfty,+%5Cinfty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-8798" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 8798"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?t - 5 = -{y} {\left(t + 4\right)} {\left(t - 1\right)} - {y'} e^{\left(5 \, t\right)} \hspace{2em} x( -5 )= -2" alt="t - 5 = -{y} {\left(t + 4\right)} {\left(t - 1\right)} - {y'} e^{\left(5 \, t\right)} \hspace{2em} x( -5 )= -2" title="t - 5 = -{y} {\left(t + 4\right)} {\left(t - 1\right)} - {y'} e^{\left(5 \, t\right)} \hspace{2em} x( -5 )= -2" data-latex="t - 5 = -{y} {\left(t + 4\right)} {\left(t - 1\right)} - {y'} e^{\left(5 \, t\right)} \hspace{2em} x( -5 )= -2"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?t%20-%205%20=%20-%7By%7D%20%7B%5Cleft(t%20+%204%5Cright)%7D%20%7B%5Cleft(t%20-%201%5Cright)%7D%20-%20%7By'%7D%20e%5E%7B%5Cleft(5%20%5C,%20t%5Cright)%7D%20%5Chspace%7B2em%7D%20x(%20-5%20)=%20-2" alt="t - 5 = -{y} {\left(t + 4\right)} {\left(t - 1\right)} - {y'} e^{\left(5 \, t\right)} \hspace{2em} x( -5 )= -2" title="t - 5 = -{y} {\left(t + 4\right)} {\left(t - 1\right)} - {y'} e^{\left(5 \, t\right)} \hspace{2em} x( -5 )= -2" data-latex="t - 5 = -{y} {\left(t + 4\right)} {\left(t - 1\right)} - {y'} e^{\left(5 \, t\right)} \hspace{2em} x( -5 )= -2"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-\infty,+\infty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-%5Cinfty,+%5Cinfty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-1333" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 1333"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-{\left(t - 5\right)} {y} e^{t} - {\left(t^{2} + 16\right)} {y'} = {\left(t + 5\right)} t \hspace{2em} x( 0 )= 2" alt="-{\left(t - 5\right)} {y} e^{t} - {\left(t^{2} + 16\right)} {y'} = {\left(t + 5\right)} t \hspace{2em} x( 0 )= 2" title="-{\left(t - 5\right)} {y} e^{t} - {\left(t^{2} + 16\right)} {y'} = {\left(t + 5\right)} t \hspace{2em} x( 0 )= 2" data-latex="-{\left(t - 5\right)} {y} e^{t} - {\left(t^{2} + 16\right)} {y'} = {\left(t + 5\right)} t \hspace{2em} x( 0 )= 2"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-%7B%5Cleft(t%20-%205%5Cright)%7D%20%7By%7D%20e%5E%7Bt%7D%20-%20%7B%5Cleft(t%5E%7B2%7D%20+%2016%5Cright)%7D%20%7By'%7D%20=%20%7B%5Cleft(t%20+%205%5Cright)%7D%20t%20%5Chspace%7B2em%7D%20x(%200%20)=%202" alt="-{\left(t - 5\right)} {y} e^{t} - {\left(t^{2} + 16\right)} {y'} = {\left(t + 5\right)} t \hspace{2em} x( 0 )= 2" title="-{\left(t - 5\right)} {y} e^{t} - {\left(t^{2} + 16\right)} {y'} = {\left(t + 5\right)} t \hspace{2em} x( 0 )= 2" data-latex="-{\left(t - 5\right)} {y} e^{t} - {\left(t^{2} + 16\right)} {y'} = {\left(t + 5\right)} t \hspace{2em} x( 0 )= 2"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-\infty,+\infty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-%5Cinfty,+%5Cinfty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-2203" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 2203"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{\left(t^{2} + 16\right)} {y} = -{\left(t - 2\right)} {\left(t - 6\right)} {y'} - t - 6 \hspace{2em} x( 4 )= 10" alt="{\left(t^{2} + 16\right)} {y} = -{\left(t - 2\right)} {\left(t - 6\right)} {y'} - t - 6 \hspace{2em} x( 4 )= 10" title="{\left(t^{2} + 16\right)} {y} = -{\left(t - 2\right)} {\left(t - 6\right)} {y'} - t - 6 \hspace{2em} x( 4 )= 10" data-latex="{\left(t^{2} + 16\right)} {y} = -{\left(t - 2\right)} {\left(t - 6\right)} {y'} - t - 6 \hspace{2em} x( 4 )= 10"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%7B%5Cleft(t%5E%7B2%7D%20+%2016%5Cright)%7D%20%7By%7D%20=%20-%7B%5Cleft(t%20-%202%5Cright)%7D%20%7B%5Cleft(t%20-%206%5Cright)%7D%20%7By'%7D%20-%20t%20-%206%20%5Chspace%7B2em%7D%20x(%204%20)=%2010" alt="{\left(t^{2} + 16\right)} {y} = -{\left(t - 2\right)} {\left(t - 6\right)} {y'} - t - 6 \hspace{2em} x( 4 )= 10" title="{\left(t^{2} + 16\right)} {y} = -{\left(t - 2\right)} {\left(t - 6\right)} {y'} - t - 6 \hspace{2em} x( 4 )= 10" data-latex="{\left(t^{2} + 16\right)} {y} = -{\left(t - 2\right)} {\left(t - 6\right)} {y'} - t - 6 \hspace{2em} x( 4 )= 10"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(2,6)" alt="(2,6)" title="(2,6)" data-latex="(2,6)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(2,6)" alt="(2,6)" title="(2,6)" data-latex="(2,6)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-2908" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 2908"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?0 = {\left(t^{2} + 1\right)} {y'} + {y} {\left(t - 1\right)} + {\left(t + 6\right)} {\left(t - 5\right)} \hspace{2em} x( 0 )= 3" alt="0 = {\left(t^{2} + 1\right)} {y'} + {y} {\left(t - 1\right)} + {\left(t + 6\right)} {\left(t - 5\right)} \hspace{2em} x( 0 )= 3" title="0 = {\left(t^{2} + 1\right)} {y'} + {y} {\left(t - 1\right)} + {\left(t + 6\right)} {\left(t - 5\right)} \hspace{2em} x( 0 )= 3" data-latex="0 = {\left(t^{2} + 1\right)} {y'} + {y} {\left(t - 1\right)} + {\left(t + 6\right)} {\left(t - 5\right)} \hspace{2em} x( 0 )= 3"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?0%20=%20%7B%5Cleft(t%5E%7B2%7D%20+%201%5Cright)%7D%20%7By'%7D%20+%20%7By%7D%20%7B%5Cleft(t%20-%201%5Cright)%7D%20+%20%7B%5Cleft(t%20+%206%5Cright)%7D%20%7B%5Cleft(t%20-%205%5Cright)%7D%20%5Chspace%7B2em%7D%20x(%200%20)=%203" alt="0 = {\left(t^{2} + 1\right)} {y'} + {y} {\left(t - 1\right)} + {\left(t + 6\right)} {\left(t - 5\right)} \hspace{2em} x( 0 )= 3" title="0 = {\left(t^{2} + 1\right)} {y'} + {y} {\left(t - 1\right)} + {\left(t + 6\right)} {\left(t - 5\right)} \hspace{2em} x( 0 )= 3" data-latex="0 = {\left(t^{2} + 1\right)} {y'} + {y} {\left(t - 1\right)} + {\left(t + 6\right)} {\left(t - 5\right)} \hspace{2em} x( 0 )= 3"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-\infty,+\infty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-%5Cinfty,+%5Cinfty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-5206" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 5206"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{\left(t + 4\right)} {\left(t - 5\right)} {y'} + t^{2} + 4 = -{\left(t + 1\right)} {y} e^{t} \hspace{2em} x( 0 )= 8" alt="{\left(t + 4\right)} {\left(t - 5\right)} {y'} + t^{2} + 4 = -{\left(t + 1\right)} {y} e^{t} \hspace{2em} x( 0 )= 8" title="{\left(t + 4\right)} {\left(t - 5\right)} {y'} + t^{2} + 4 = -{\left(t + 1\right)} {y} e^{t} \hspace{2em} x( 0 )= 8" data-latex="{\left(t + 4\right)} {\left(t - 5\right)} {y'} + t^{2} + 4 = -{\left(t + 1\right)} {y} e^{t} \hspace{2em} x( 0 )= 8"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%7B%5Cleft(t%20+%204%5Cright)%7D%20%7B%5Cleft(t%20-%205%5Cright)%7D%20%7By'%7D%20+%20t%5E%7B2%7D%20+%204%20=%20-%7B%5Cleft(t%20+%201%5Cright)%7D%20%7By%7D%20e%5E%7Bt%7D%20%5Chspace%7B2em%7D%20x(%200%20)=%208" alt="{\left(t + 4\right)} {\left(t - 5\right)} {y'} + t^{2} + 4 = -{\left(t + 1\right)} {y} e^{t} \hspace{2em} x( 0 )= 8" title="{\left(t + 4\right)} {\left(t - 5\right)} {y'} + t^{2} + 4 = -{\left(t + 1\right)} {y} e^{t} \hspace{2em} x( 0 )= 8" data-latex="{\left(t + 4\right)} {\left(t - 5\right)} {y'} + t^{2} + 4 = -{\left(t + 1\right)} {y} e^{t} \hspace{2em} x( 0 )= 8"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-4,5)" alt="(-4,5)" title="(-4,5)" data-latex="(-4,5)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-4,5)" alt="(-4,5)" title="(-4,5)" data-latex="(-4,5)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-8900" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 8900"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y} {\left(t + 4\right)} {\left(t - 6\right)} + {y'} e^{\left(-3 \, t\right)} = -{\left(t + 2\right)} e^{t} \hspace{2em} x( -2 )= 5" alt="{y} {\left(t + 4\right)} {\left(t - 6\right)} + {y'} e^{\left(-3 \, t\right)} = -{\left(t + 2\right)} e^{t} \hspace{2em} x( -2 )= 5" title="{y} {\left(t + 4\right)} {\left(t - 6\right)} + {y'} e^{\left(-3 \, t\right)} = -{\left(t + 2\right)} e^{t} \hspace{2em} x( -2 )= 5" data-latex="{y} {\left(t + 4\right)} {\left(t - 6\right)} + {y'} e^{\left(-3 \, t\right)} = -{\left(t + 2\right)} e^{t} \hspace{2em} x( -2 )= 5"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%7By%7D%20%7B%5Cleft(t%20+%204%5Cright)%7D%20%7B%5Cleft(t%20-%206%5Cright)%7D%20+%20%7By'%7D%20e%5E%7B%5Cleft(-3%20%5C,%20t%5Cright)%7D%20=%20-%7B%5Cleft(t%20+%202%5Cright)%7D%20e%5E%7Bt%7D%20%5Chspace%7B2em%7D%20x(%20-2%20)=%205" alt="{y} {\left(t + 4\right)} {\left(t - 6\right)} + {y'} e^{\left(-3 \, t\right)} = -{\left(t + 2\right)} e^{t} \hspace{2em} x( -2 )= 5" title="{y} {\left(t + 4\right)} {\left(t - 6\right)} + {y'} e^{\left(-3 \, t\right)} = -{\left(t + 2\right)} e^{t} \hspace{2em} x( -2 )= 5" data-latex="{y} {\left(t + 4\right)} {\left(t - 6\right)} + {y'} e^{\left(-3 \, t\right)} = -{\left(t + 2\right)} e^{t} \hspace{2em} x( -2 )= 5"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-\infty,+\infty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-%5Cinfty,+%5Cinfty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-5586" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 5586"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-{\left(t - 6\right)} t = {y'} {\left(t + 6\right)} + {y} e^{\left(-4 \, t\right)} \hspace{2em} x( -4 )= -10" alt="-{\left(t - 6\right)} t = {y'} {\left(t + 6\right)} + {y} e^{\left(-4 \, t\right)} \hspace{2em} x( -4 )= -10" title="-{\left(t - 6\right)} t = {y'} {\left(t + 6\right)} + {y} e^{\left(-4 \, t\right)} \hspace{2em} x( -4 )= -10" data-latex="-{\left(t - 6\right)} t = {y'} {\left(t + 6\right)} + {y} e^{\left(-4 \, t\right)} \hspace{2em} x( -4 )= -10"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-%7B%5Cleft(t%20-%206%5Cright)%7D%20t%20=%20%7By'%7D%20%7B%5Cleft(t%20+%206%5Cright)%7D%20+%20%7By%7D%20e%5E%7B%5Cleft(-4%20%5C,%20t%5Cright)%7D%20%5Chspace%7B2em%7D%20x(%20-4%20)=%20-10" alt="-{\left(t - 6\right)} t = {y'} {\left(t + 6\right)} + {y} e^{\left(-4 \, t\right)} \hspace{2em} x( -4 )= -10" title="-{\left(t - 6\right)} t = {y'} {\left(t + 6\right)} + {y} e^{\left(-4 \, t\right)} \hspace{2em} x( -4 )= -10" data-latex="-{\left(t - 6\right)} t = {y'} {\left(t + 6\right)} + {y} e^{\left(-4 \, t\right)} \hspace{2em} x( -4 )= -10"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-6,+\infty)" alt="(-6,+\infty)" title="(-6,+\infty)" data-latex="(-6,+\infty)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-6,+%5Cinfty)" alt="(-6,+\infty)" title="(-6,+\infty)" data-latex="(-6,+\infty)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-1028" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 1028"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y} {\left(t + 2\right)} + {\left(t + 6\right)} {\left(t - 6\right)} = -{\left(t^{2} + 16\right)} {y'} \hspace{2em} x( 1 )= 3" alt="{y} {\left(t + 2\right)} + {\left(t + 6\right)} {\left(t - 6\right)} = -{\left(t^{2} + 16\right)} {y'} \hspace{2em} x( 1 )= 3" title="{y} {\left(t + 2\right)} + {\left(t + 6\right)} {\left(t - 6\right)} = -{\left(t^{2} + 16\right)} {y'} \hspace{2em} x( 1 )= 3" data-latex="{y} {\left(t + 2\right)} + {\left(t + 6\right)} {\left(t - 6\right)} = -{\left(t^{2} + 16\right)} {y'} \hspace{2em} x( 1 )= 3"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%7By%7D%20%7B%5Cleft(t%20+%202%5Cright)%7D%20+%20%7B%5Cleft(t%20+%206%5Cright)%7D%20%7B%5Cleft(t%20-%206%5Cright)%7D%20=%20-%7B%5Cleft(t%5E%7B2%7D%20+%2016%5Cright)%7D%20%7By'%7D%20%5Chspace%7B2em%7D%20x(%201%20)=%203" alt="{y} {\left(t + 2\right)} + {\left(t + 6\right)} {\left(t - 6\right)} = -{\left(t^{2} + 16\right)} {y'} \hspace{2em} x( 1 )= 3" title="{y} {\left(t + 2\right)} + {\left(t + 6\right)} {\left(t - 6\right)} = -{\left(t^{2} + 16\right)} {y'} \hspace{2em} x( 1 )= 3" data-latex="{y} {\left(t + 2\right)} + {\left(t + 6\right)} {\left(t - 6\right)} = -{\left(t^{2} + 16\right)} {y'} \hspace{2em} x( 1 )= 3"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-\infty,+\infty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-%5Cinfty,+%5Cinfty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-3260" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 3260"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?0 = {\left(t + 5\right)} {\left(t - 2\right)} {y} + {y'} e^{\left(3 \, t\right)} + t - 5 \hspace{2em} x( 3 )= -4" alt="0 = {\left(t + 5\right)} {\left(t - 2\right)} {y} + {y'} e^{\left(3 \, t\right)} + t - 5 \hspace{2em} x( 3 )= -4" title="0 = {\left(t + 5\right)} {\left(t - 2\right)} {y} + {y'} e^{\left(3 \, t\right)} + t - 5 \hspace{2em} x( 3 )= -4" data-latex="0 = {\left(t + 5\right)} {\left(t - 2\right)} {y} + {y'} e^{\left(3 \, t\right)} + t - 5 \hspace{2em} x( 3 )= -4"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?0%20=%20%7B%5Cleft(t%20+%205%5Cright)%7D%20%7B%5Cleft(t%20-%202%5Cright)%7D%20%7By%7D%20+%20%7By'%7D%20e%5E%7B%5Cleft(3%20%5C,%20t%5Cright)%7D%20+%20t%20-%205%20%5Chspace%7B2em%7D%20x(%203%20)=%20-4" alt="0 = {\left(t + 5\right)} {\left(t - 2\right)} {y} + {y'} e^{\left(3 \, t\right)} + t - 5 \hspace{2em} x( 3 )= -4" title="0 = {\left(t + 5\right)} {\left(t - 2\right)} {y} + {y'} e^{\left(3 \, t\right)} + t - 5 \hspace{2em} x( 3 )= -4" data-latex="0 = {\left(t + 5\right)} {\left(t - 2\right)} {y} + {y'} e^{\left(3 \, t\right)} + t - 5 \hspace{2em} x( 3 )= -4"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-\infty,+\infty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-%5Cinfty,+%5Cinfty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-6031" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 6031"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y'} {\left(t + 6\right)} + {\left(t - 5\right)} t = -{\left(t^{2} + 9\right)} {y} \hspace{2em} x( -9 )= -2" alt="{y'} {\left(t + 6\right)} + {\left(t - 5\right)} t = -{\left(t^{2} + 9\right)} {y} \hspace{2em} x( -9 )= -2" title="{y'} {\left(t + 6\right)} + {\left(t - 5\right)} t = -{\left(t^{2} + 9\right)} {y} \hspace{2em} x( -9 )= -2" data-latex="{y'} {\left(t + 6\right)} + {\left(t - 5\right)} t = -{\left(t^{2} + 9\right)} {y} \hspace{2em} x( -9 )= -2"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%7By'%7D%20%7B%5Cleft(t%20+%206%5Cright)%7D%20+%20%7B%5Cleft(t%20-%205%5Cright)%7D%20t%20=%20-%7B%5Cleft(t%5E%7B2%7D%20+%209%5Cright)%7D%20%7By%7D%20%5Chspace%7B2em%7D%20x(%20-9%20)=%20-2" alt="{y'} {\left(t + 6\right)} + {\left(t - 5\right)} t = -{\left(t^{2} + 9\right)} {y} \hspace{2em} x( -9 )= -2" title="{y'} {\left(t + 6\right)} + {\left(t - 5\right)} t = -{\left(t^{2} + 9\right)} {y} \hspace{2em} x( -9 )= -2" data-latex="{y'} {\left(t + 6\right)} + {\left(t - 5\right)} t = -{\left(t^{2} + 9\right)} {y} \hspace{2em} x( -9 )= -2"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-\infty,-6)" alt="(-\infty,-6)" title="(-\infty,-6)" data-latex="(-\infty,-6)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-%5Cinfty,-6)" alt="(-\infty,-6)" title="(-\infty,-6)" data-latex="(-\infty,-6)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-1382" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 1382"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-{\left(t^{2} + 9\right)} {y} = {y'} {\left(t - 1\right)} e^{t} + {\left(t + 4\right)} {\left(t - 6\right)} \hspace{2em} x( -3 )= 2" alt="-{\left(t^{2} + 9\right)} {y} = {y'} {\left(t - 1\right)} e^{t} + {\left(t + 4\right)} {\left(t - 6\right)} \hspace{2em} x( -3 )= 2" title="-{\left(t^{2} + 9\right)} {y} = {y'} {\left(t - 1\right)} e^{t} + {\left(t + 4\right)} {\left(t - 6\right)} \hspace{2em} x( -3 )= 2" data-latex="-{\left(t^{2} + 9\right)} {y} = {y'} {\left(t - 1\right)} e^{t} + {\left(t + 4\right)} {\left(t - 6\right)} \hspace{2em} x( -3 )= 2"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-%7B%5Cleft(t%5E%7B2%7D%20+%209%5Cright)%7D%20%7By%7D%20=%20%7By'%7D%20%7B%5Cleft(t%20-%201%5Cright)%7D%20e%5E%7Bt%7D%20+%20%7B%5Cleft(t%20+%204%5Cright)%7D%20%7B%5Cleft(t%20-%206%5Cright)%7D%20%5Chspace%7B2em%7D%20x(%20-3%20)=%202" alt="-{\left(t^{2} + 9\right)} {y} = {y'} {\left(t - 1\right)} e^{t} + {\left(t + 4\right)} {\left(t - 6\right)} \hspace{2em} x( -3 )= 2" title="-{\left(t^{2} + 9\right)} {y} = {y'} {\left(t - 1\right)} e^{t} + {\left(t + 4\right)} {\left(t - 6\right)} \hspace{2em} x( -3 )= 2" data-latex="-{\left(t^{2} + 9\right)} {y} = {y'} {\left(t - 1\right)} e^{t} + {\left(t + 4\right)} {\left(t - 6\right)} \hspace{2em} x( -3 )= 2"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-\infty,1)" alt="(-\infty,1)" title="(-\infty,1)" data-latex="(-\infty,1)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-%5Cinfty,1)" alt="(-\infty,1)" title="(-\infty,1)" data-latex="(-\infty,1)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-8567" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 8567"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?t^{2} + 1 = -{\left(t + 5\right)} {\left(t - 5\right)} {y'} - {\left(t + 2\right)} {y} \hspace{2em} x( -2 )= 7" alt="t^{2} + 1 = -{\left(t + 5\right)} {\left(t - 5\right)} {y'} - {\left(t + 2\right)} {y} \hspace{2em} x( -2 )= 7" title="t^{2} + 1 = -{\left(t + 5\right)} {\left(t - 5\right)} {y'} - {\left(t + 2\right)} {y} \hspace{2em} x( -2 )= 7" data-latex="t^{2} + 1 = -{\left(t + 5\right)} {\left(t - 5\right)} {y'} - {\left(t + 2\right)} {y} \hspace{2em} x( -2 )= 7"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?t%5E%7B2%7D%20+%201%20=%20-%7B%5Cleft(t%20+%205%5Cright)%7D%20%7B%5Cleft(t%20-%205%5Cright)%7D%20%7By'%7D%20-%20%7B%5Cleft(t%20+%202%5Cright)%7D%20%7By%7D%20%5Chspace%7B2em%7D%20x(%20-2%20)=%207" alt="t^{2} + 1 = -{\left(t + 5\right)} {\left(t - 5\right)} {y'} - {\left(t + 2\right)} {y} \hspace{2em} x( -2 )= 7" title="t^{2} + 1 = -{\left(t + 5\right)} {\left(t - 5\right)} {y'} - {\left(t + 2\right)} {y} \hspace{2em} x( -2 )= 7" data-latex="t^{2} + 1 = -{\left(t + 5\right)} {\left(t - 5\right)} {y'} - {\left(t + 2\right)} {y} \hspace{2em} x( -2 )= 7"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-5,5)" alt="(-5,5)" title="(-5,5)" data-latex="(-5,5)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-5,5)" alt="(-5,5)" title="(-5,5)" data-latex="(-5,5)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-9101" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 9101"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y} {\left(t + 4\right)} {\left(t - 5\right)} = -{y'} {\left(t + 2\right)} e^{t} - t^{2} - 25 \hspace{2em} x( -3 )= -1" alt="{y} {\left(t + 4\right)} {\left(t - 5\right)} = -{y'} {\left(t + 2\right)} e^{t} - t^{2} - 25 \hspace{2em} x( -3 )= -1" title="{y} {\left(t + 4\right)} {\left(t - 5\right)} = -{y'} {\left(t + 2\right)} e^{t} - t^{2} - 25 \hspace{2em} x( -3 )= -1" data-latex="{y} {\left(t + 4\right)} {\left(t - 5\right)} = -{y'} {\left(t + 2\right)} e^{t} - t^{2} - 25 \hspace{2em} x( -3 )= -1"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%7By%7D%20%7B%5Cleft(t%20+%204%5Cright)%7D%20%7B%5Cleft(t%20-%205%5Cright)%7D%20=%20-%7By'%7D%20%7B%5Cleft(t%20+%202%5Cright)%7D%20e%5E%7Bt%7D%20-%20t%5E%7B2%7D%20-%2025%20%5Chspace%7B2em%7D%20x(%20-3%20)=%20-1" alt="{y} {\left(t + 4\right)} {\left(t - 5\right)} = -{y'} {\left(t + 2\right)} e^{t} - t^{2} - 25 \hspace{2em} x( -3 )= -1" title="{y} {\left(t + 4\right)} {\left(t - 5\right)} = -{y'} {\left(t + 2\right)} e^{t} - t^{2} - 25 \hspace{2em} x( -3 )= -1" data-latex="{y} {\left(t + 4\right)} {\left(t - 5\right)} = -{y'} {\left(t + 2\right)} e^{t} - t^{2} - 25 \hspace{2em} x( -3 )= -1"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-\infty,-2)" alt="(-\infty,-2)" title="(-\infty,-2)" data-latex="(-\infty,-2)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-%5Cinfty,-2)" alt="(-\infty,-2)" title="(-\infty,-2)" data-latex="(-\infty,-2)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-9555" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 9555"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-{y} {\left(t + 6\right)} {\left(t - 5\right)} - {\left(t^{2} + 25\right)} {y'} = {\left(t - 1\right)} e^{t} \hspace{2em} x( -1 )= 6" alt="-{y} {\left(t + 6\right)} {\left(t - 5\right)} - {\left(t^{2} + 25\right)} {y'} = {\left(t - 1\right)} e^{t} \hspace{2em} x( -1 )= 6" title="-{y} {\left(t + 6\right)} {\left(t - 5\right)} - {\left(t^{2} + 25\right)} {y'} = {\left(t - 1\right)} e^{t} \hspace{2em} x( -1 )= 6" data-latex="-{y} {\left(t + 6\right)} {\left(t - 5\right)} - {\left(t^{2} + 25\right)} {y'} = {\left(t - 1\right)} e^{t} \hspace{2em} x( -1 )= 6"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-%7By%7D%20%7B%5Cleft(t%20+%206%5Cright)%7D%20%7B%5Cleft(t%20-%205%5Cright)%7D%20-%20%7B%5Cleft(t%5E%7B2%7D%20+%2025%5Cright)%7D%20%7By'%7D%20=%20%7B%5Cleft(t%20-%201%5Cright)%7D%20e%5E%7Bt%7D%20%5Chspace%7B2em%7D%20x(%20-1%20)=%206" alt="-{y} {\left(t + 6\right)} {\left(t - 5\right)} - {\left(t^{2} + 25\right)} {y'} = {\left(t - 1\right)} e^{t} \hspace{2em} x( -1 )= 6" title="-{y} {\left(t + 6\right)} {\left(t - 5\right)} - {\left(t^{2} + 25\right)} {y'} = {\left(t - 1\right)} e^{t} \hspace{2em} x( -1 )= 6" data-latex="-{y} {\left(t + 6\right)} {\left(t - 5\right)} - {\left(t^{2} + 25\right)} {y'} = {\left(t - 1\right)} e^{t} \hspace{2em} x( -1 )= 6"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-\infty,+\infty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-%5Cinfty,+%5Cinfty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-6265" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 6265"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-{y'} {\left(t + 4\right)} {\left(t - 2\right)} - {\left(t^{2} + 9\right)} {y} - {\left(t - 6\right)} e^{t} = 0 \hspace{2em} x( -3 )= 3" alt="-{y'} {\left(t + 4\right)} {\left(t - 2\right)} - {\left(t^{2} + 9\right)} {y} - {\left(t - 6\right)} e^{t} = 0 \hspace{2em} x( -3 )= 3" title="-{y'} {\left(t + 4\right)} {\left(t - 2\right)} - {\left(t^{2} + 9\right)} {y} - {\left(t - 6\right)} e^{t} = 0 \hspace{2em} x( -3 )= 3" data-latex="-{y'} {\left(t + 4\right)} {\left(t - 2\right)} - {\left(t^{2} + 9\right)} {y} - {\left(t - 6\right)} e^{t} = 0 \hspace{2em} x( -3 )= 3"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-%7By'%7D%20%7B%5Cleft(t%20+%204%5Cright)%7D%20%7B%5Cleft(t%20-%202%5Cright)%7D%20-%20%7B%5Cleft(t%5E%7B2%7D%20+%209%5Cright)%7D%20%7By%7D%20-%20%7B%5Cleft(t%20-%206%5Cright)%7D%20e%5E%7Bt%7D%20=%200%20%5Chspace%7B2em%7D%20x(%20-3%20)=%203" alt="-{y'} {\left(t + 4\right)} {\left(t - 2\right)} - {\left(t^{2} + 9\right)} {y} - {\left(t - 6\right)} e^{t} = 0 \hspace{2em} x( -3 )= 3" title="-{y'} {\left(t + 4\right)} {\left(t - 2\right)} - {\left(t^{2} + 9\right)} {y} - {\left(t - 6\right)} e^{t} = 0 \hspace{2em} x( -3 )= 3" data-latex="-{y'} {\left(t + 4\right)} {\left(t - 2\right)} - {\left(t^{2} + 9\right)} {y} - {\left(t - 6\right)} e^{t} = 0 \hspace{2em} x( -3 )= 3"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-4,2)" alt="(-4,2)" title="(-4,2)" data-latex="(-4,2)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-4,2)" alt="(-4,2)" title="(-4,2)" data-latex="(-4,2)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-6588" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 6588"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y} {\left(t + 4\right)} + {\left(t + 1\right)} {\left(t - 5\right)} = -{y'} e^{\left(-2 \, t\right)} \hspace{2em} x( 2 )= -6" alt="{y} {\left(t + 4\right)} + {\left(t + 1\right)} {\left(t - 5\right)} = -{y'} e^{\left(-2 \, t\right)} \hspace{2em} x( 2 )= -6" title="{y} {\left(t + 4\right)} + {\left(t + 1\right)} {\left(t - 5\right)} = -{y'} e^{\left(-2 \, t\right)} \hspace{2em} x( 2 )= -6" data-latex="{y} {\left(t + 4\right)} + {\left(t + 1\right)} {\left(t - 5\right)} = -{y'} e^{\left(-2 \, t\right)} \hspace{2em} x( 2 )= -6"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%7By%7D%20%7B%5Cleft(t%20+%204%5Cright)%7D%20+%20%7B%5Cleft(t%20+%201%5Cright)%7D%20%7B%5Cleft(t%20-%205%5Cright)%7D%20=%20-%7By'%7D%20e%5E%7B%5Cleft(-2%20%5C,%20t%5Cright)%7D%20%5Chspace%7B2em%7D%20x(%202%20)=%20-6" alt="{y} {\left(t + 4\right)} + {\left(t + 1\right)} {\left(t - 5\right)} = -{y'} e^{\left(-2 \, t\right)} \hspace{2em} x( 2 )= -6" title="{y} {\left(t + 4\right)} + {\left(t + 1\right)} {\left(t - 5\right)} = -{y'} e^{\left(-2 \, t\right)} \hspace{2em} x( 2 )= -6" data-latex="{y} {\left(t + 4\right)} + {\left(t + 1\right)} {\left(t - 5\right)} = -{y'} e^{\left(-2 \, t\right)} \hspace{2em} x( 2 )= -6"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-\infty,+\infty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-%5Cinfty,+%5Cinfty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-5988" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 5988"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y} {\left(t + 5\right)} {\left(t + 1\right)} + e^{t} = -{y'} {\left(t - 5\right)} e^{t} \hspace{2em} x( 8 )= 2" alt="{y} {\left(t + 5\right)} {\left(t + 1\right)} + e^{t} = -{y'} {\left(t - 5\right)} e^{t} \hspace{2em} x( 8 )= 2" title="{y} {\left(t + 5\right)} {\left(t + 1\right)} + e^{t} = -{y'} {\left(t - 5\right)} e^{t} \hspace{2em} x( 8 )= 2" data-latex="{y} {\left(t + 5\right)} {\left(t + 1\right)} + e^{t} = -{y'} {\left(t - 5\right)} e^{t} \hspace{2em} x( 8 )= 2"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%7By%7D%20%7B%5Cleft(t%20+%205%5Cright)%7D%20%7B%5Cleft(t%20+%201%5Cright)%7D%20+%20e%5E%7Bt%7D%20=%20-%7By'%7D%20%7B%5Cleft(t%20-%205%5Cright)%7D%20e%5E%7Bt%7D%20%5Chspace%7B2em%7D%20x(%208%20)=%202" alt="{y} {\left(t + 5\right)} {\left(t + 1\right)} + e^{t} = -{y'} {\left(t - 5\right)} e^{t} \hspace{2em} x( 8 )= 2" title="{y} {\left(t + 5\right)} {\left(t + 1\right)} + e^{t} = -{y'} {\left(t - 5\right)} e^{t} \hspace{2em} x( 8 )= 2" data-latex="{y} {\left(t + 5\right)} {\left(t + 1\right)} + e^{t} = -{y'} {\left(t - 5\right)} e^{t} \hspace{2em} x( 8 )= 2"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(5,+\infty)" alt="(5,+\infty)" title="(5,+\infty)" data-latex="(5,+\infty)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(5,+%5Cinfty)" alt="(5,+\infty)" title="(5,+\infty)" data-latex="(5,+\infty)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-4080" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 4080"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{\left(t + 5\right)} {y'} e^{t} + {\left(t - 1\right)} {\left(t - 5\right)} + {\left(t^{2} + 9\right)} {y} = 0 \hspace{2em} x( -2 )= -9" alt="{\left(t + 5\right)} {y'} e^{t} + {\left(t - 1\right)} {\left(t - 5\right)} + {\left(t^{2} + 9\right)} {y} = 0 \hspace{2em} x( -2 )= -9" title="{\left(t + 5\right)} {y'} e^{t} + {\left(t - 1\right)} {\left(t - 5\right)} + {\left(t^{2} + 9\right)} {y} = 0 \hspace{2em} x( -2 )= -9" data-latex="{\left(t + 5\right)} {y'} e^{t} + {\left(t - 1\right)} {\left(t - 5\right)} + {\left(t^{2} + 9\right)} {y} = 0 \hspace{2em} x( -2 )= -9"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%7B%5Cleft(t%20+%205%5Cright)%7D%20%7By'%7D%20e%5E%7Bt%7D%20+%20%7B%5Cleft(t%20-%201%5Cright)%7D%20%7B%5Cleft(t%20-%205%5Cright)%7D%20+%20%7B%5Cleft(t%5E%7B2%7D%20+%209%5Cright)%7D%20%7By%7D%20=%200%20%5Chspace%7B2em%7D%20x(%20-2%20)=%20-9" alt="{\left(t + 5\right)} {y'} e^{t} + {\left(t - 1\right)} {\left(t - 5\right)} + {\left(t^{2} + 9\right)} {y} = 0 \hspace{2em} x( -2 )= -9" title="{\left(t + 5\right)} {y'} e^{t} + {\left(t - 1\right)} {\left(t - 5\right)} + {\left(t^{2} + 9\right)} {y} = 0 \hspace{2em} x( -2 )= -9" data-latex="{\left(t + 5\right)} {y'} e^{t} + {\left(t - 1\right)} {\left(t - 5\right)} + {\left(t^{2} + 9\right)} {y} = 0 \hspace{2em} x( -2 )= -9"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-5,+\infty)" alt="(-5,+\infty)" title="(-5,+\infty)" data-latex="(-5,+\infty)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-5,+%5Cinfty)" alt="(-5,+\infty)" title="(-5,+\infty)" data-latex="(-5,+\infty)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-7739" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 7739"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-{\left(t + 5\right)} {\left(t - 5\right)} = {y'} {\left(t + 1\right)} + {y} e^{\left(4 \, t\right)} \hspace{2em} x( -4 )= 0" alt="-{\left(t + 5\right)} {\left(t - 5\right)} = {y'} {\left(t + 1\right)} + {y} e^{\left(4 \, t\right)} \hspace{2em} x( -4 )= 0" title="-{\left(t + 5\right)} {\left(t - 5\right)} = {y'} {\left(t + 1\right)} + {y} e^{\left(4 \, t\right)} \hspace{2em} x( -4 )= 0" data-latex="-{\left(t + 5\right)} {\left(t - 5\right)} = {y'} {\left(t + 1\right)} + {y} e^{\left(4 \, t\right)} \hspace{2em} x( -4 )= 0"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-%7B%5Cleft(t%20+%205%5Cright)%7D%20%7B%5Cleft(t%20-%205%5Cright)%7D%20=%20%7By'%7D%20%7B%5Cleft(t%20+%201%5Cright)%7D%20+%20%7By%7D%20e%5E%7B%5Cleft(4%20%5C,%20t%5Cright)%7D%20%5Chspace%7B2em%7D%20x(%20-4%20)=%200" alt="-{\left(t + 5\right)} {\left(t - 5\right)} = {y'} {\left(t + 1\right)} + {y} e^{\left(4 \, t\right)} \hspace{2em} x( -4 )= 0" title="-{\left(t + 5\right)} {\left(t - 5\right)} = {y'} {\left(t + 1\right)} + {y} e^{\left(4 \, t\right)} \hspace{2em} x( -4 )= 0" data-latex="-{\left(t + 5\right)} {\left(t - 5\right)} = {y'} {\left(t + 1\right)} + {y} e^{\left(4 \, t\right)} \hspace{2em} x( -4 )= 0"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-\infty,-1)" alt="(-\infty,-1)" title="(-\infty,-1)" data-latex="(-\infty,-1)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-%5Cinfty,-1)" alt="(-\infty,-1)" title="(-\infty,-1)" data-latex="(-\infty,-1)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-6189" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 6189"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y'} {\left(t + 4\right)} {\left(t - 5\right)} = -{y} e^{\left(5 \, t\right)} - {\left(t - 1\right)} e^{t} \hspace{2em} x( 2 )= 9" alt="{y'} {\left(t + 4\right)} {\left(t - 5\right)} = -{y} e^{\left(5 \, t\right)} - {\left(t - 1\right)} e^{t} \hspace{2em} x( 2 )= 9" title="{y'} {\left(t + 4\right)} {\left(t - 5\right)} = -{y} e^{\left(5 \, t\right)} - {\left(t - 1\right)} e^{t} \hspace{2em} x( 2 )= 9" data-latex="{y'} {\left(t + 4\right)} {\left(t - 5\right)} = -{y} e^{\left(5 \, t\right)} - {\left(t - 1\right)} e^{t} \hspace{2em} x( 2 )= 9"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%7By'%7D%20%7B%5Cleft(t%20+%204%5Cright)%7D%20%7B%5Cleft(t%20-%205%5Cright)%7D%20=%20-%7By%7D%20e%5E%7B%5Cleft(5%20%5C,%20t%5Cright)%7D%20-%20%7B%5Cleft(t%20-%201%5Cright)%7D%20e%5E%7Bt%7D%20%5Chspace%7B2em%7D%20x(%202%20)=%209" alt="{y'} {\left(t + 4\right)} {\left(t - 5\right)} = -{y} e^{\left(5 \, t\right)} - {\left(t - 1\right)} e^{t} \hspace{2em} x( 2 )= 9" title="{y'} {\left(t + 4\right)} {\left(t - 5\right)} = -{y} e^{\left(5 \, t\right)} - {\left(t - 1\right)} e^{t} \hspace{2em} x( 2 )= 9" data-latex="{y'} {\left(t + 4\right)} {\left(t - 5\right)} = -{y} e^{\left(5 \, t\right)} - {\left(t - 1\right)} e^{t} \hspace{2em} x( 2 )= 9"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-4,5)" alt="(-4,5)" title="(-4,5)" data-latex="(-4,5)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-4,5)" alt="(-4,5)" title="(-4,5)" data-latex="(-4,5)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-6776" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 6776"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?0 = {\left(t + 4\right)} {\left(t - 1\right)} + {y'} {\left(t - 6\right)} + {y} e^{\left(3 \, t\right)} \hspace{2em} x( 8 )= 4" alt="0 = {\left(t + 4\right)} {\left(t - 1\right)} + {y'} {\left(t - 6\right)} + {y} e^{\left(3 \, t\right)} \hspace{2em} x( 8 )= 4" title="0 = {\left(t + 4\right)} {\left(t - 1\right)} + {y'} {\left(t - 6\right)} + {y} e^{\left(3 \, t\right)} \hspace{2em} x( 8 )= 4" data-latex="0 = {\left(t + 4\right)} {\left(t - 1\right)} + {y'} {\left(t - 6\right)} + {y} e^{\left(3 \, t\right)} \hspace{2em} x( 8 )= 4"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?0%20=%20%7B%5Cleft(t%20+%204%5Cright)%7D%20%7B%5Cleft(t%20-%201%5Cright)%7D%20+%20%7By'%7D%20%7B%5Cleft(t%20-%206%5Cright)%7D%20+%20%7By%7D%20e%5E%7B%5Cleft(3%20%5C,%20t%5Cright)%7D%20%5Chspace%7B2em%7D%20x(%208%20)=%204" alt="0 = {\left(t + 4\right)} {\left(t - 1\right)} + {y'} {\left(t - 6\right)} + {y} e^{\left(3 \, t\right)} \hspace{2em} x( 8 )= 4" title="0 = {\left(t + 4\right)} {\left(t - 1\right)} + {y'} {\left(t - 6\right)} + {y} e^{\left(3 \, t\right)} \hspace{2em} x( 8 )= 4" data-latex="0 = {\left(t + 4\right)} {\left(t - 1\right)} + {y'} {\left(t - 6\right)} + {y} e^{\left(3 \, t\right)} \hspace{2em} x( 8 )= 4"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(6,+\infty)" alt="(6,+\infty)" title="(6,+\infty)" data-latex="(6,+\infty)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(6,+%5Cinfty)" alt="(6,+\infty)" title="(6,+\infty)" data-latex="(6,+\infty)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-9560" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 9560"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?0 = {\left(t + 6\right)} {\left(t - 5\right)} {y} + {y'} e^{\left(-4 \, t\right)} + t - 2 \hspace{2em} x( 2 )= -2" alt="0 = {\left(t + 6\right)} {\left(t - 5\right)} {y} + {y'} e^{\left(-4 \, t\right)} + t - 2 \hspace{2em} x( 2 )= -2" title="0 = {\left(t + 6\right)} {\left(t - 5\right)} {y} + {y'} e^{\left(-4 \, t\right)} + t - 2 \hspace{2em} x( 2 )= -2" data-latex="0 = {\left(t + 6\right)} {\left(t - 5\right)} {y} + {y'} e^{\left(-4 \, t\right)} + t - 2 \hspace{2em} x( 2 )= -2"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?0%20=%20%7B%5Cleft(t%20+%206%5Cright)%7D%20%7B%5Cleft(t%20-%205%5Cright)%7D%20%7By%7D%20+%20%7By'%7D%20e%5E%7B%5Cleft(-4%20%5C,%20t%5Cright)%7D%20+%20t%20-%202%20%5Chspace%7B2em%7D%20x(%202%20)=%20-2" alt="0 = {\left(t + 6\right)} {\left(t - 5\right)} {y} + {y'} e^{\left(-4 \, t\right)} + t - 2 \hspace{2em} x( 2 )= -2" title="0 = {\left(t + 6\right)} {\left(t - 5\right)} {y} + {y'} e^{\left(-4 \, t\right)} + t - 2 \hspace{2em} x( 2 )= -2" data-latex="0 = {\left(t + 6\right)} {\left(t - 5\right)} {y} + {y'} e^{\left(-4 \, t\right)} + t - 2 \hspace{2em} x( 2 )= -2"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-\infty,+\infty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-%5Cinfty,+%5Cinfty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-6033" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 6033"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-t^{2} - {\left(t + 4\right)} {y'} - 16 = {\left(t - 1\right)} {\left(t - 6\right)} {y} \hspace{2em} x( -1 )= -7" alt="-t^{2} - {\left(t + 4\right)} {y'} - 16 = {\left(t - 1\right)} {\left(t - 6\right)} {y} \hspace{2em} x( -1 )= -7" title="-t^{2} - {\left(t + 4\right)} {y'} - 16 = {\left(t - 1\right)} {\left(t - 6\right)} {y} \hspace{2em} x( -1 )= -7" data-latex="-t^{2} - {\left(t + 4\right)} {y'} - 16 = {\left(t - 1\right)} {\left(t - 6\right)} {y} \hspace{2em} x( -1 )= -7"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-t%5E%7B2%7D%20-%20%7B%5Cleft(t%20+%204%5Cright)%7D%20%7By'%7D%20-%2016%20=%20%7B%5Cleft(t%20-%201%5Cright)%7D%20%7B%5Cleft(t%20-%206%5Cright)%7D%20%7By%7D%20%5Chspace%7B2em%7D%20x(%20-1%20)=%20-7" alt="-t^{2} - {\left(t + 4\right)} {y'} - 16 = {\left(t - 1\right)} {\left(t - 6\right)} {y} \hspace{2em} x( -1 )= -7" title="-t^{2} - {\left(t + 4\right)} {y'} - 16 = {\left(t - 1\right)} {\left(t - 6\right)} {y} \hspace{2em} x( -1 )= -7" data-latex="-t^{2} - {\left(t + 4\right)} {y'} - 16 = {\left(t - 1\right)} {\left(t - 6\right)} {y} \hspace{2em} x( -1 )= -7"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-4,+\infty)" alt="(-4,+\infty)" title="(-4,+\infty)" data-latex="(-4,+\infty)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-4,+%5Cinfty)" alt="(-4,+\infty)" title="(-4,+\infty)" data-latex="(-4,+\infty)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-0066" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 0066"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-{y'} {\left(t + 2\right)} {\left(t - 5\right)} - {y} {\left(t + 5\right)} e^{t} - t^{2} - 4 = 0 \hspace{2em} x( -1 )= 6" alt="-{y'} {\left(t + 2\right)} {\left(t - 5\right)} - {y} {\left(t + 5\right)} e^{t} - t^{2} - 4 = 0 \hspace{2em} x( -1 )= 6" title="-{y'} {\left(t + 2\right)} {\left(t - 5\right)} - {y} {\left(t + 5\right)} e^{t} - t^{2} - 4 = 0 \hspace{2em} x( -1 )= 6" data-latex="-{y'} {\left(t + 2\right)} {\left(t - 5\right)} - {y} {\left(t + 5\right)} e^{t} - t^{2} - 4 = 0 \hspace{2em} x( -1 )= 6"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-%7By'%7D%20%7B%5Cleft(t%20+%202%5Cright)%7D%20%7B%5Cleft(t%20-%205%5Cright)%7D%20-%20%7By%7D%20%7B%5Cleft(t%20+%205%5Cright)%7D%20e%5E%7Bt%7D%20-%20t%5E%7B2%7D%20-%204%20=%200%20%5Chspace%7B2em%7D%20x(%20-1%20)=%206" alt="-{y'} {\left(t + 2\right)} {\left(t - 5\right)} - {y} {\left(t + 5\right)} e^{t} - t^{2} - 4 = 0 \hspace{2em} x( -1 )= 6" title="-{y'} {\left(t + 2\right)} {\left(t - 5\right)} - {y} {\left(t + 5\right)} e^{t} - t^{2} - 4 = 0 \hspace{2em} x( -1 )= 6" data-latex="-{y'} {\left(t + 2\right)} {\left(t - 5\right)} - {y} {\left(t + 5\right)} e^{t} - t^{2} - 4 = 0 \hspace{2em} x( -1 )= 6"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-2,5)" alt="(-2,5)" title="(-2,5)" data-latex="(-2,5)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-2,5)" alt="(-2,5)" title="(-2,5)" data-latex="(-2,5)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-4499" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 4499"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-{y} {\left(t + 4\right)} {\left(t - 5\right)} - {y'} {\left(t - 1\right)} e^{t} = t^{2} + 16 \hspace{2em} x( 5 )= 0" alt="-{y} {\left(t + 4\right)} {\left(t - 5\right)} - {y'} {\left(t - 1\right)} e^{t} = t^{2} + 16 \hspace{2em} x( 5 )= 0" title="-{y} {\left(t + 4\right)} {\left(t - 5\right)} - {y'} {\left(t - 1\right)} e^{t} = t^{2} + 16 \hspace{2em} x( 5 )= 0" data-latex="-{y} {\left(t + 4\right)} {\left(t - 5\right)} - {y'} {\left(t - 1\right)} e^{t} = t^{2} + 16 \hspace{2em} x( 5 )= 0"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-%7By%7D%20%7B%5Cleft(t%20+%204%5Cright)%7D%20%7B%5Cleft(t%20-%205%5Cright)%7D%20-%20%7By'%7D%20%7B%5Cleft(t%20-%201%5Cright)%7D%20e%5E%7Bt%7D%20=%20t%5E%7B2%7D%20+%2016%20%5Chspace%7B2em%7D%20x(%205%20)=%200" alt="-{y} {\left(t + 4\right)} {\left(t - 5\right)} - {y'} {\left(t - 1\right)} e^{t} = t^{2} + 16 \hspace{2em} x( 5 )= 0" title="-{y} {\left(t + 4\right)} {\left(t - 5\right)} - {y'} {\left(t - 1\right)} e^{t} = t^{2} + 16 \hspace{2em} x( 5 )= 0" data-latex="-{y} {\left(t + 4\right)} {\left(t - 5\right)} - {y'} {\left(t - 1\right)} e^{t} = t^{2} + 16 \hspace{2em} x( 5 )= 0"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(1,+\infty)" alt="(1,+\infty)" title="(1,+\infty)" data-latex="(1,+\infty)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(1,+%5Cinfty)" alt="(1,+\infty)" title="(1,+\infty)" data-latex="(1,+\infty)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-3320" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 3320"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-{y'} {\left(t + 4\right)} e^{t} - t^{2} - 1 = {y} {\left(t - 2\right)} {\left(t - 5\right)} \hspace{2em} x( 0 )= -5" alt="-{y'} {\left(t + 4\right)} e^{t} - t^{2} - 1 = {y} {\left(t - 2\right)} {\left(t - 5\right)} \hspace{2em} x( 0 )= -5" title="-{y'} {\left(t + 4\right)} e^{t} - t^{2} - 1 = {y} {\left(t - 2\right)} {\left(t - 5\right)} \hspace{2em} x( 0 )= -5" data-latex="-{y'} {\left(t + 4\right)} e^{t} - t^{2} - 1 = {y} {\left(t - 2\right)} {\left(t - 5\right)} \hspace{2em} x( 0 )= -5"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-%7By'%7D%20%7B%5Cleft(t%20+%204%5Cright)%7D%20e%5E%7Bt%7D%20-%20t%5E%7B2%7D%20-%201%20=%20%7By%7D%20%7B%5Cleft(t%20-%202%5Cright)%7D%20%7B%5Cleft(t%20-%205%5Cright)%7D%20%5Chspace%7B2em%7D%20x(%200%20)=%20-5" alt="-{y'} {\left(t + 4\right)} e^{t} - t^{2} - 1 = {y} {\left(t - 2\right)} {\left(t - 5\right)} \hspace{2em} x( 0 )= -5" title="-{y'} {\left(t + 4\right)} e^{t} - t^{2} - 1 = {y} {\left(t - 2\right)} {\left(t - 5\right)} \hspace{2em} x( 0 )= -5" data-latex="-{y'} {\left(t + 4\right)} e^{t} - t^{2} - 1 = {y} {\left(t - 2\right)} {\left(t - 5\right)} \hspace{2em} x( 0 )= -5"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-4,+\infty)" alt="(-4,+\infty)" title="(-4,+\infty)" data-latex="(-4,+\infty)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-4,+%5Cinfty)" alt="(-4,+\infty)" title="(-4,+\infty)" data-latex="(-4,+\infty)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-7531" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 7531"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-{y} e^{\left(-3 \, t\right)} - t + 6 = {y'} {\left(t + 5\right)} {\left(t - 2\right)} \hspace{2em} x( 0 )= 6" alt="-{y} e^{\left(-3 \, t\right)} - t + 6 = {y'} {\left(t + 5\right)} {\left(t - 2\right)} \hspace{2em} x( 0 )= 6" title="-{y} e^{\left(-3 \, t\right)} - t + 6 = {y'} {\left(t + 5\right)} {\left(t - 2\right)} \hspace{2em} x( 0 )= 6" data-latex="-{y} e^{\left(-3 \, t\right)} - t + 6 = {y'} {\left(t + 5\right)} {\left(t - 2\right)} \hspace{2em} x( 0 )= 6"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-%7By%7D%20e%5E%7B%5Cleft(-3%20%5C,%20t%5Cright)%7D%20-%20t%20+%206%20=%20%7By'%7D%20%7B%5Cleft(t%20+%205%5Cright)%7D%20%7B%5Cleft(t%20-%202%5Cright)%7D%20%5Chspace%7B2em%7D%20x(%200%20)=%206" alt="-{y} e^{\left(-3 \, t\right)} - t + 6 = {y'} {\left(t + 5\right)} {\left(t - 2\right)} \hspace{2em} x( 0 )= 6" title="-{y} e^{\left(-3 \, t\right)} - t + 6 = {y'} {\left(t + 5\right)} {\left(t - 2\right)} \hspace{2em} x( 0 )= 6" data-latex="-{y} e^{\left(-3 \, t\right)} - t + 6 = {y'} {\left(t + 5\right)} {\left(t - 2\right)} \hspace{2em} x( 0 )= 6"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-5,2)" alt="(-5,2)" title="(-5,2)" data-latex="(-5,2)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-5,2)" alt="(-5,2)" title="(-5,2)" data-latex="(-5,2)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-7982" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 7982"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-{y} {\left(t + 5\right)} {\left(t - 6\right)} = {y'} {\left(t - 2\right)} e^{t} + t^{2} + 9 \hspace{2em} x( -1 )= 6" alt="-{y} {\left(t + 5\right)} {\left(t - 6\right)} = {y'} {\left(t - 2\right)} e^{t} + t^{2} + 9 \hspace{2em} x( -1 )= 6" title="-{y} {\left(t + 5\right)} {\left(t - 6\right)} = {y'} {\left(t - 2\right)} e^{t} + t^{2} + 9 \hspace{2em} x( -1 )= 6" data-latex="-{y} {\left(t + 5\right)} {\left(t - 6\right)} = {y'} {\left(t - 2\right)} e^{t} + t^{2} + 9 \hspace{2em} x( -1 )= 6"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-%7By%7D%20%7B%5Cleft(t%20+%205%5Cright)%7D%20%7B%5Cleft(t%20-%206%5Cright)%7D%20=%20%7By'%7D%20%7B%5Cleft(t%20-%202%5Cright)%7D%20e%5E%7Bt%7D%20+%20t%5E%7B2%7D%20+%209%20%5Chspace%7B2em%7D%20x(%20-1%20)=%206" alt="-{y} {\left(t + 5\right)} {\left(t - 6\right)} = {y'} {\left(t - 2\right)} e^{t} + t^{2} + 9 \hspace{2em} x( -1 )= 6" title="-{y} {\left(t + 5\right)} {\left(t - 6\right)} = {y'} {\left(t - 2\right)} e^{t} + t^{2} + 9 \hspace{2em} x( -1 )= 6" data-latex="-{y} {\left(t + 5\right)} {\left(t - 6\right)} = {y'} {\left(t - 2\right)} e^{t} + t^{2} + 9 \hspace{2em} x( -1 )= 6"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-\infty,2)" alt="(-\infty,2)" title="(-\infty,2)" data-latex="(-\infty,2)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-%5Cinfty,2)" alt="(-\infty,2)" title="(-\infty,2)" data-latex="(-\infty,2)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-4739" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 4739"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-{y} {\left(t + 5\right)} e^{t} - {\left(t - 5\right)} t - {y'} e^{\left(-t\right)} = 0 \hspace{2em} x( 3 )= -3" alt="-{y} {\left(t + 5\right)} e^{t} - {\left(t - 5\right)} t - {y'} e^{\left(-t\right)} = 0 \hspace{2em} x( 3 )= -3" title="-{y} {\left(t + 5\right)} e^{t} - {\left(t - 5\right)} t - {y'} e^{\left(-t\right)} = 0 \hspace{2em} x( 3 )= -3" data-latex="-{y} {\left(t + 5\right)} e^{t} - {\left(t - 5\right)} t - {y'} e^{\left(-t\right)} = 0 \hspace{2em} x( 3 )= -3"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-%7By%7D%20%7B%5Cleft(t%20+%205%5Cright)%7D%20e%5E%7Bt%7D%20-%20%7B%5Cleft(t%20-%205%5Cright)%7D%20t%20-%20%7By'%7D%20e%5E%7B%5Cleft(-t%5Cright)%7D%20=%200%20%5Chspace%7B2em%7D%20x(%203%20)=%20-3" alt="-{y} {\left(t + 5\right)} e^{t} - {\left(t - 5\right)} t - {y'} e^{\left(-t\right)} = 0 \hspace{2em} x( 3 )= -3" title="-{y} {\left(t + 5\right)} e^{t} - {\left(t - 5\right)} t - {y'} e^{\left(-t\right)} = 0 \hspace{2em} x( 3 )= -3" data-latex="-{y} {\left(t + 5\right)} e^{t} - {\left(t - 5\right)} t - {y'} e^{\left(-t\right)} = 0 \hspace{2em} x( 3 )= -3"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-\infty,+\infty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-%5Cinfty,+%5Cinfty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-0472" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 0472"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?0 = -{\left(t + 6\right)} t {y'} - {\left(t - 6\right)} {y} e^{t} - t^{2} - 16 \hspace{2em} x( -5 )= -10" alt="0 = -{\left(t + 6\right)} t {y'} - {\left(t - 6\right)} {y} e^{t} - t^{2} - 16 \hspace{2em} x( -5 )= -10" title="0 = -{\left(t + 6\right)} t {y'} - {\left(t - 6\right)} {y} e^{t} - t^{2} - 16 \hspace{2em} x( -5 )= -10" data-latex="0 = -{\left(t + 6\right)} t {y'} - {\left(t - 6\right)} {y} e^{t} - t^{2} - 16 \hspace{2em} x( -5 )= -10"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?0%20=%20-%7B%5Cleft(t%20+%206%5Cright)%7D%20t%20%7By'%7D%20-%20%7B%5Cleft(t%20-%206%5Cright)%7D%20%7By%7D%20e%5E%7Bt%7D%20-%20t%5E%7B2%7D%20-%2016%20%5Chspace%7B2em%7D%20x(%20-5%20)=%20-10" alt="0 = -{\left(t + 6\right)} t {y'} - {\left(t - 6\right)} {y} e^{t} - t^{2} - 16 \hspace{2em} x( -5 )= -10" title="0 = -{\left(t + 6\right)} t {y'} - {\left(t - 6\right)} {y} e^{t} - t^{2} - 16 \hspace{2em} x( -5 )= -10" data-latex="0 = -{\left(t + 6\right)} t {y'} - {\left(t - 6\right)} {y} e^{t} - t^{2} - 16 \hspace{2em} x( -5 )= -10"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-6,0)" alt="(-6,0)" title="(-6,0)" data-latex="(-6,0)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-6,0)" alt="(-6,0)" title="(-6,0)" data-latex="(-6,0)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-9676" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 9676"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{\left(t + 2\right)} {\left(t - 5\right)} {y} + e^{\left(-4 \, t\right)} = -{\left(t + 6\right)} {y'} \hspace{2em} x( -2 )= -8" alt="{\left(t + 2\right)} {\left(t - 5\right)} {y} + e^{\left(-4 \, t\right)} = -{\left(t + 6\right)} {y'} \hspace{2em} x( -2 )= -8" title="{\left(t + 2\right)} {\left(t - 5\right)} {y} + e^{\left(-4 \, t\right)} = -{\left(t + 6\right)} {y'} \hspace{2em} x( -2 )= -8" data-latex="{\left(t + 2\right)} {\left(t - 5\right)} {y} + e^{\left(-4 \, t\right)} = -{\left(t + 6\right)} {y'} \hspace{2em} x( -2 )= -8"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%7B%5Cleft(t%20+%202%5Cright)%7D%20%7B%5Cleft(t%20-%205%5Cright)%7D%20%7By%7D%20+%20e%5E%7B%5Cleft(-4%20%5C,%20t%5Cright)%7D%20=%20-%7B%5Cleft(t%20+%206%5Cright)%7D%20%7By'%7D%20%5Chspace%7B2em%7D%20x(%20-2%20)=%20-8" alt="{\left(t + 2\right)} {\left(t - 5\right)} {y} + e^{\left(-4 \, t\right)} = -{\left(t + 6\right)} {y'} \hspace{2em} x( -2 )= -8" title="{\left(t + 2\right)} {\left(t - 5\right)} {y} + e^{\left(-4 \, t\right)} = -{\left(t + 6\right)} {y'} \hspace{2em} x( -2 )= -8" data-latex="{\left(t + 2\right)} {\left(t - 5\right)} {y} + e^{\left(-4 \, t\right)} = -{\left(t + 6\right)} {y'} \hspace{2em} x( -2 )= -8"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-6,+\infty)" alt="(-6,+\infty)" title="(-6,+\infty)" data-latex="(-6,+\infty)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-6,+%5Cinfty)" alt="(-6,+\infty)" title="(-6,+\infty)" data-latex="(-6,+\infty)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-5885" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 5885"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-{y'} {\left(t - 5\right)} e^{t} - e^{t} = {y} {\left(t + 6\right)} t \hspace{2em} x( 1 )= 7" alt="-{y'} {\left(t - 5\right)} e^{t} - e^{t} = {y} {\left(t + 6\right)} t \hspace{2em} x( 1 )= 7" title="-{y'} {\left(t - 5\right)} e^{t} - e^{t} = {y} {\left(t + 6\right)} t \hspace{2em} x( 1 )= 7" data-latex="-{y'} {\left(t - 5\right)} e^{t} - e^{t} = {y} {\left(t + 6\right)} t \hspace{2em} x( 1 )= 7"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-%7By'%7D%20%7B%5Cleft(t%20-%205%5Cright)%7D%20e%5E%7Bt%7D%20-%20e%5E%7Bt%7D%20=%20%7By%7D%20%7B%5Cleft(t%20+%206%5Cright)%7D%20t%20%5Chspace%7B2em%7D%20x(%201%20)=%207" alt="-{y'} {\left(t - 5\right)} e^{t} - e^{t} = {y} {\left(t + 6\right)} t \hspace{2em} x( 1 )= 7" title="-{y'} {\left(t - 5\right)} e^{t} - e^{t} = {y} {\left(t + 6\right)} t \hspace{2em} x( 1 )= 7" data-latex="-{y'} {\left(t - 5\right)} e^{t} - e^{t} = {y} {\left(t + 6\right)} t \hspace{2em} x( 1 )= 7"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-\infty,5)" alt="(-\infty,5)" title="(-\infty,5)" data-latex="(-\infty,5)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-%5Cinfty,5)" alt="(-\infty,5)" title="(-\infty,5)" data-latex="(-\infty,5)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-7854" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 7854"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y'} {\left(t + 4\right)} {\left(t - 1\right)} + {y} e^{\left(-2 \, t\right)} = -{\left(t - 6\right)} e^{t} \hspace{2em} x( 0 )= 4" alt="{y'} {\left(t + 4\right)} {\left(t - 1\right)} + {y} e^{\left(-2 \, t\right)} = -{\left(t - 6\right)} e^{t} \hspace{2em} x( 0 )= 4" title="{y'} {\left(t + 4\right)} {\left(t - 1\right)} + {y} e^{\left(-2 \, t\right)} = -{\left(t - 6\right)} e^{t} \hspace{2em} x( 0 )= 4" data-latex="{y'} {\left(t + 4\right)} {\left(t - 1\right)} + {y} e^{\left(-2 \, t\right)} = -{\left(t - 6\right)} e^{t} \hspace{2em} x( 0 )= 4"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%7By'%7D%20%7B%5Cleft(t%20+%204%5Cright)%7D%20%7B%5Cleft(t%20-%201%5Cright)%7D%20+%20%7By%7D%20e%5E%7B%5Cleft(-2%20%5C,%20t%5Cright)%7D%20=%20-%7B%5Cleft(t%20-%206%5Cright)%7D%20e%5E%7Bt%7D%20%5Chspace%7B2em%7D%20x(%200%20)=%204" alt="{y'} {\left(t + 4\right)} {\left(t - 1\right)} + {y} e^{\left(-2 \, t\right)} = -{\left(t - 6\right)} e^{t} \hspace{2em} x( 0 )= 4" title="{y'} {\left(t + 4\right)} {\left(t - 1\right)} + {y} e^{\left(-2 \, t\right)} = -{\left(t - 6\right)} e^{t} \hspace{2em} x( 0 )= 4" data-latex="{y'} {\left(t + 4\right)} {\left(t - 1\right)} + {y} e^{\left(-2 \, t\right)} = -{\left(t - 6\right)} e^{t} \hspace{2em} x( 0 )= 4"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-4,1)" alt="(-4,1)" title="(-4,1)" data-latex="(-4,1)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-4,1)" alt="(-4,1)" title="(-4,1)" data-latex="(-4,1)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-4003" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 4003"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?0 = -{y'} {\left(t + 1\right)} - {\left(t + 4\right)} {\left(t - 6\right)} - {y} e^{\left(-4 \, t\right)} \hspace{2em} x( -5 )= 2" alt="0 = -{y'} {\left(t + 1\right)} - {\left(t + 4\right)} {\left(t - 6\right)} - {y} e^{\left(-4 \, t\right)} \hspace{2em} x( -5 )= 2" title="0 = -{y'} {\left(t + 1\right)} - {\left(t + 4\right)} {\left(t - 6\right)} - {y} e^{\left(-4 \, t\right)} \hspace{2em} x( -5 )= 2" data-latex="0 = -{y'} {\left(t + 1\right)} - {\left(t + 4\right)} {\left(t - 6\right)} - {y} e^{\left(-4 \, t\right)} \hspace{2em} x( -5 )= 2"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?0%20=%20-%7By'%7D%20%7B%5Cleft(t%20+%201%5Cright)%7D%20-%20%7B%5Cleft(t%20+%204%5Cright)%7D%20%7B%5Cleft(t%20-%206%5Cright)%7D%20-%20%7By%7D%20e%5E%7B%5Cleft(-4%20%5C,%20t%5Cright)%7D%20%5Chspace%7B2em%7D%20x(%20-5%20)=%202" alt="0 = -{y'} {\left(t + 1\right)} - {\left(t + 4\right)} {\left(t - 6\right)} - {y} e^{\left(-4 \, t\right)} \hspace{2em} x( -5 )= 2" title="0 = -{y'} {\left(t + 1\right)} - {\left(t + 4\right)} {\left(t - 6\right)} - {y} e^{\left(-4 \, t\right)} \hspace{2em} x( -5 )= 2" data-latex="0 = -{y'} {\left(t + 1\right)} - {\left(t + 4\right)} {\left(t - 6\right)} - {y} e^{\left(-4 \, t\right)} \hspace{2em} x( -5 )= 2"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-\infty,-1)" alt="(-\infty,-1)" title="(-\infty,-1)" data-latex="(-\infty,-1)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-%5Cinfty,-1)" alt="(-\infty,-1)" title="(-\infty,-1)" data-latex="(-\infty,-1)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-4821" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 4821"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{\left(t^{2} + 4\right)} {y} = -{\left(t + 6\right)} {\left(t - 2\right)} {y'} - t + 5 \hspace{2em} x( -1 )= -8" alt="{\left(t^{2} + 4\right)} {y} = -{\left(t + 6\right)} {\left(t - 2\right)} {y'} - t + 5 \hspace{2em} x( -1 )= -8" title="{\left(t^{2} + 4\right)} {y} = -{\left(t + 6\right)} {\left(t - 2\right)} {y'} - t + 5 \hspace{2em} x( -1 )= -8" data-latex="{\left(t^{2} + 4\right)} {y} = -{\left(t + 6\right)} {\left(t - 2\right)} {y'} - t + 5 \hspace{2em} x( -1 )= -8"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%7B%5Cleft(t%5E%7B2%7D%20+%204%5Cright)%7D%20%7By%7D%20=%20-%7B%5Cleft(t%20+%206%5Cright)%7D%20%7B%5Cleft(t%20-%202%5Cright)%7D%20%7By'%7D%20-%20t%20+%205%20%5Chspace%7B2em%7D%20x(%20-1%20)=%20-8" alt="{\left(t^{2} + 4\right)} {y} = -{\left(t + 6\right)} {\left(t - 2\right)} {y'} - t + 5 \hspace{2em} x( -1 )= -8" title="{\left(t^{2} + 4\right)} {y} = -{\left(t + 6\right)} {\left(t - 2\right)} {y'} - t + 5 \hspace{2em} x( -1 )= -8" data-latex="{\left(t^{2} + 4\right)} {y} = -{\left(t + 6\right)} {\left(t - 2\right)} {y'} - t + 5 \hspace{2em} x( -1 )= -8"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-6,2)" alt="(-6,2)" title="(-6,2)" data-latex="(-6,2)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-6,2)" alt="(-6,2)" title="(-6,2)" data-latex="(-6,2)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-3670" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 3670"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?0 = -{y'} {\left(t + 6\right)} - {\left(t - 2\right)} {\left(t - 5\right)} - {y} e^{\left(5 \, t\right)} \hspace{2em} x( -5 )= -8" alt="0 = -{y'} {\left(t + 6\right)} - {\left(t - 2\right)} {\left(t - 5\right)} - {y} e^{\left(5 \, t\right)} \hspace{2em} x( -5 )= -8" title="0 = -{y'} {\left(t + 6\right)} - {\left(t - 2\right)} {\left(t - 5\right)} - {y} e^{\left(5 \, t\right)} \hspace{2em} x( -5 )= -8" data-latex="0 = -{y'} {\left(t + 6\right)} - {\left(t - 2\right)} {\left(t - 5\right)} - {y} e^{\left(5 \, t\right)} \hspace{2em} x( -5 )= -8"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?0%20=%20-%7By'%7D%20%7B%5Cleft(t%20+%206%5Cright)%7D%20-%20%7B%5Cleft(t%20-%202%5Cright)%7D%20%7B%5Cleft(t%20-%205%5Cright)%7D%20-%20%7By%7D%20e%5E%7B%5Cleft(5%20%5C,%20t%5Cright)%7D%20%5Chspace%7B2em%7D%20x(%20-5%20)=%20-8" alt="0 = -{y'} {\left(t + 6\right)} - {\left(t - 2\right)} {\left(t - 5\right)} - {y} e^{\left(5 \, t\right)} \hspace{2em} x( -5 )= -8" title="0 = -{y'} {\left(t + 6\right)} - {\left(t - 2\right)} {\left(t - 5\right)} - {y} e^{\left(5 \, t\right)} \hspace{2em} x( -5 )= -8" data-latex="0 = -{y'} {\left(t + 6\right)} - {\left(t - 2\right)} {\left(t - 5\right)} - {y} e^{\left(5 \, t\right)} \hspace{2em} x( -5 )= -8"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-6,+\infty)" alt="(-6,+\infty)" title="(-6,+\infty)" data-latex="(-6,+\infty)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-6,+%5Cinfty)" alt="(-6,+\infty)" title="(-6,+\infty)" data-latex="(-6,+\infty)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-5169" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 5169"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y} t + {y'} e^{\left(-t\right)} = -{\left(t + 6\right)} {\left(t - 5\right)} \hspace{2em} x( -3 )= 1" alt="{y} t + {y'} e^{\left(-t\right)} = -{\left(t + 6\right)} {\left(t - 5\right)} \hspace{2em} x( -3 )= 1" title="{y} t + {y'} e^{\left(-t\right)} = -{\left(t + 6\right)} {\left(t - 5\right)} \hspace{2em} x( -3 )= 1" data-latex="{y} t + {y'} e^{\left(-t\right)} = -{\left(t + 6\right)} {\left(t - 5\right)} \hspace{2em} x( -3 )= 1"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%7By%7D%20t%20+%20%7By'%7D%20e%5E%7B%5Cleft(-t%5Cright)%7D%20=%20-%7B%5Cleft(t%20+%206%5Cright)%7D%20%7B%5Cleft(t%20-%205%5Cright)%7D%20%5Chspace%7B2em%7D%20x(%20-3%20)=%201" alt="{y} t + {y'} e^{\left(-t\right)} = -{\left(t + 6\right)} {\left(t - 5\right)} \hspace{2em} x( -3 )= 1" title="{y} t + {y'} e^{\left(-t\right)} = -{\left(t + 6\right)} {\left(t - 5\right)} \hspace{2em} x( -3 )= 1" data-latex="{y} t + {y'} e^{\left(-t\right)} = -{\left(t + 6\right)} {\left(t - 5\right)} \hspace{2em} x( -3 )= 1"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-\infty,+\infty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-%5Cinfty,+%5Cinfty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="N1-7192" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 7192"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>N1.</strong></p><p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. </p><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-{y} {\left(t + 4\right)} {\left(t - 5\right)} - {y'} e^{\left(-4 \, t\right)} = {\left(t - 2\right)} e^{t} \hspace{2em} x( 6 )= 1" alt="-{y} {\left(t + 4\right)} {\left(t - 5\right)} - {y'} e^{\left(-4 \, t\right)} = {\left(t - 2\right)} e^{t} \hspace{2em} x( 6 )= 1" title="-{y} {\left(t + 4\right)} {\left(t - 5\right)} - {y'} e^{\left(-4 \, t\right)} = {\left(t - 2\right)} e^{t} \hspace{2em} x( 6 )= 1" data-latex="-{y} {\left(t + 4\right)} {\left(t - 5\right)} - {y'} e^{\left(-4 \, t\right)} = {\left(t - 2\right)} e^{t} \hspace{2em} x( 6 )= 1"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following IVP. &lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-%7By%7D%20%7B%5Cleft(t%20+%204%5Cright)%7D%20%7B%5Cleft(t%20-%205%5Cright)%7D%20-%20%7By'%7D%20e%5E%7B%5Cleft(-4%20%5C,%20t%5Cright)%7D%20=%20%7B%5Cleft(t%20-%202%5Cright)%7D%20e%5E%7Bt%7D%20%5Chspace%7B2em%7D%20x(%206%20)=%201" alt="-{y} {\left(t + 4\right)} {\left(t - 5\right)} - {y'} e^{\left(-4 \, t\right)} = {\left(t - 2\right)} e^{t} \hspace{2em} x( 6 )= 1" title="-{y} {\left(t + 4\right)} {\left(t - 5\right)} - {y'} e^{\left(-4 \, t\right)} = {\left(t - 2\right)} e^{t} \hspace{2em} x( 6 )= 1" data-latex="-{y} {\left(t + 4\right)} {\left(t - 5\right)} - {y'} e^{\left(-4 \, t\right)} = {\left(t - 2\right)} e^{t} \hspace{2em} x( 6 )= 1"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-\infty,+\infty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-%5Cinfty,+%5Cinfty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item></objectbank>
</questestinterop>