CoCalc -- F3.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="F3">
    <qtimetadata>
      <qtimetadatafield><fieldlabel>bank_title</fieldlabel><fieldentry>Differential Equations -- F3</fieldentry></qtimetadatafield>
    </qtimetadata>
  <item ident="F3-4749" title="F3 | Techniques for linear IVPs | ver. 4749"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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?-5 \, {y} - \frac{24}{t^{3}} = -{y'} t \hspace{2em} y( 1 )= 0" alt="-5 \, {y} - \frac{24}{t^{3}} = -{y'} t \hspace{2em} y( 1 )= 0" title="-5 \, {y} - \frac{24}{t^{3}} = -{y'} t \hspace{2em} y( 1 )= 0" data-latex="-5 \, {y} - \frac{24}{t^{3}} = -{y'} t \hspace{2em} y( 1 )= 0"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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?-5%20%5C,%20%7By%7D%20-%20%5Cfrac%7B24%7D%7Bt%5E%7B3%7D%7D%20=%20-%7By'%7D%20t%20%5Chspace%7B2em%7D%20y(%201%20)=%200" alt="-5 \, {y} - \frac{24}{t^{3}} = -{y'} t \hspace{2em} y( 1 )= 0" title="-5 \, {y} - \frac{24}{t^{3}} = -{y'} t \hspace{2em} y( 1 )= 0" data-latex="-5 \, {y} - \frac{24}{t^{3}} = -{y'} t \hspace{2em} y( 1 )= 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?{y} = 3 \, t^{5} - \frac{3}{t^{3}}" alt="{y} = 3 \, t^{5} - \frac{3}{t^{3}}" title="{y} = 3 \, t^{5} - \frac{3}{t^{3}}" data-latex="{y} = 3 \, t^{5} - \frac{3}{t^{3}}"/></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?%7By%7D%20=%203%20%5C,%20t%5E%7B5%7D%20-%20%5Cfrac%7B3%7D%7Bt%5E%7B3%7D%7D" alt="{y} = 3 \, t^{5} - \frac{3}{t^{3}}" title="{y} = 3 \, t^{5} - \frac{3}{t^{3}}" data-latex="{y} = 3 \, t^{5} - \frac{3}{t^{3}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-3627" title="F3 | Techniques for linear IVPs | ver. 3627"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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 - 2 \, {y} + 12 \, t = 0 \hspace{2em} y( 1 )= 5" alt="-{y'} t - 2 \, {y} + 12 \, t = 0 \hspace{2em} y( 1 )= 5" title="-{y'} t - 2 \, {y} + 12 \, t = 0 \hspace{2em} y( 1 )= 5" data-latex="-{y'} t - 2 \, {y} + 12 \, t = 0 \hspace{2em} y( 1 )= 5"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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-%202%20%5C,%20%7By%7D%20+%2012%20%5C,%20t%20=%200%20%5Chspace%7B2em%7D%20y(%201%20)=%205" alt="-{y'} t - 2 \, {y} + 12 \, t = 0 \hspace{2em} y( 1 )= 5" title="-{y'} t - 2 \, {y} + 12 \, t = 0 \hspace{2em} y( 1 )= 5" data-latex="-{y'} t - 2 \, {y} + 12 \, t = 0 \hspace{2em} y( 1 )= 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?{y} = 4 \, t + \frac{1}{t^{2}}" alt="{y} = 4 \, t + \frac{1}{t^{2}}" title="{y} = 4 \, t + \frac{1}{t^{2}}" data-latex="{y} = 4 \, t + \frac{1}{t^{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?%7By%7D%20=%204%20%5C,%20t%20+%20%5Cfrac%7B1%7D%7Bt%5E%7B2%7D%7D" alt="{y} = 4 \, t + \frac{1}{t^{2}}" title="{y} = 4 \, t + \frac{1}{t^{2}}" data-latex="{y} = 4 \, t + \frac{1}{t^{2}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-7961" title="F3 | Techniques for linear IVPs | ver. 7961"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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 + 3 \, t = 2 \, {y} \hspace{2em} y( -1 )= -4" alt="-{y'} t + 3 \, t = 2 \, {y} \hspace{2em} y( -1 )= -4" title="-{y'} t + 3 \, t = 2 \, {y} \hspace{2em} y( -1 )= -4" data-latex="-{y'} t + 3 \, t = 2 \, {y} \hspace{2em} y( -1 )= -4"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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+%203%20%5C,%20t%20=%202%20%5C,%20%7By%7D%20%5Chspace%7B2em%7D%20y(%20-1%20)=%20-4" alt="-{y'} t + 3 \, t = 2 \, {y} \hspace{2em} y( -1 )= -4" title="-{y'} t + 3 \, t = 2 \, {y} \hspace{2em} y( -1 )= -4" data-latex="-{y'} t + 3 \, t = 2 \, {y} \hspace{2em} y( -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?{y} = t - \frac{3}{t^{2}}" alt="{y} = t - \frac{3}{t^{2}}" title="{y} = t - \frac{3}{t^{2}}" data-latex="{y} = t - \frac{3}{t^{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?%7By%7D%20=%20t%20-%20%5Cfrac%7B3%7D%7Bt%5E%7B2%7D%7D" alt="{y} = t - \frac{3}{t^{2}}" title="{y} = t - \frac{3}{t^{2}}" data-latex="{y} = t - \frac{3}{t^{2}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-1825" title="F3 | Techniques for linear IVPs | ver. 1825"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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 + 3 \, {y} = -\frac{8}{t} \hspace{2em} y( -1 )= 1" alt="-{y'} t + 3 \, {y} = -\frac{8}{t} \hspace{2em} y( -1 )= 1" title="-{y'} t + 3 \, {y} = -\frac{8}{t} \hspace{2em} y( -1 )= 1" data-latex="-{y'} t + 3 \, {y} = -\frac{8}{t} \hspace{2em} y( -1 )= 1"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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+%203%20%5C,%20%7By%7D%20=%20-%5Cfrac%7B8%7D%7Bt%7D%20%5Chspace%7B2em%7D%20y(%20-1%20)=%201" alt="-{y'} t + 3 \, {y} = -\frac{8}{t} \hspace{2em} y( -1 )= 1" title="-{y'} t + 3 \, {y} = -\frac{8}{t} \hspace{2em} y( -1 )= 1" data-latex="-{y'} t + 3 \, {y} = -\frac{8}{t} \hspace{2em} y( -1 )= 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?{y} = t^{3} - \frac{2}{t}" alt="{y} = t^{3} - \frac{2}{t}" title="{y} = t^{3} - \frac{2}{t}" data-latex="{y} = t^{3} - \frac{2}{t}"/></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?%7By%7D%20=%20t%5E%7B3%7D%20-%20%5Cfrac%7B2%7D%7Bt%7D" alt="{y} = t^{3} - \frac{2}{t}" title="{y} = t^{3} - \frac{2}{t}" data-latex="{y} = t^{3} - \frac{2}{t}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-2171" title="F3 | Techniques for linear IVPs | ver. 2171"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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?-3 \, {y} - \frac{4}{t} = -{y'} t \hspace{2em} y( -1 )= 0" alt="-3 \, {y} - \frac{4}{t} = -{y'} t \hspace{2em} y( -1 )= 0" title="-3 \, {y} - \frac{4}{t} = -{y'} t \hspace{2em} y( -1 )= 0" data-latex="-3 \, {y} - \frac{4}{t} = -{y'} t \hspace{2em} y( -1 )= 0"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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?-3%20%5C,%20%7By%7D%20-%20%5Cfrac%7B4%7D%7Bt%7D%20=%20-%7By'%7D%20t%20%5Chspace%7B2em%7D%20y(%20-1%20)=%200" alt="-3 \, {y} - \frac{4}{t} = -{y'} t \hspace{2em} y( -1 )= 0" title="-3 \, {y} - \frac{4}{t} = -{y'} t \hspace{2em} y( -1 )= 0" data-latex="-3 \, {y} - \frac{4}{t} = -{y'} t \hspace{2em} y( -1 )= 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?{y} = t^{3} - \frac{1}{t}" alt="{y} = t^{3} - \frac{1}{t}" title="{y} = t^{3} - \frac{1}{t}" data-latex="{y} = t^{3} - \frac{1}{t}"/></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?%7By%7D%20=%20t%5E%7B3%7D%20-%20%5Cfrac%7B1%7D%7Bt%7D" alt="{y} = t^{3} - \frac{1}{t}" title="{y} = t^{3} - \frac{1}{t}" data-latex="{y} = t^{3} - \frac{1}{t}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-6294" title="F3 | Techniques for linear IVPs | ver. 6294"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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?5 \, {y} = 12 \, t^{2} + t {y'} \hspace{2em} y( -1 )= 2" alt="5 \, {y} = 12 \, t^{2} + t {y'} \hspace{2em} y( -1 )= 2" title="5 \, {y} = 12 \, t^{2} + t {y'} \hspace{2em} y( -1 )= 2" data-latex="5 \, {y} = 12 \, t^{2} + t {y'} \hspace{2em} y( -1 )= 2"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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?5%20%5C,%20%7By%7D%20=%2012%20%5C,%20t%5E%7B2%7D%20+%20t%20%7By'%7D%20%5Chspace%7B2em%7D%20y(%20-1%20)=%202" alt="5 \, {y} = 12 \, t^{2} + t {y'} \hspace{2em} y( -1 )= 2" title="5 \, {y} = 12 \, t^{2} + t {y'} \hspace{2em} y( -1 )= 2" data-latex="5 \, {y} = 12 \, t^{2} + t {y'} \hspace{2em} y( -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?{y} = 2 \, t^{5} + 4 \, t^{2}" alt="{y} = 2 \, t^{5} + 4 \, t^{2}" title="{y} = 2 \, t^{5} + 4 \, t^{2}" data-latex="{y} = 2 \, t^{5} + 4 \, t^{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?%7By%7D%20=%202%20%5C,%20t%5E%7B5%7D%20+%204%20%5C,%20t%5E%7B2%7D" alt="{y} = 2 \, t^{5} + 4 \, t^{2}" title="{y} = 2 \, t^{5} + 4 \, t^{2}" data-latex="{y} = 2 \, t^{5} + 4 \, t^{2}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-2661" title="F3 | Techniques for linear IVPs | ver. 2661"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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 - 3 \, {y} = -\frac{14}{t^{4}} \hspace{2em} y( -1 )= -2" alt="{y'} t - 3 \, {y} = -\frac{14}{t^{4}} \hspace{2em} y( -1 )= -2" title="{y'} t - 3 \, {y} = -\frac{14}{t^{4}} \hspace{2em} y( -1 )= -2" data-latex="{y'} t - 3 \, {y} = -\frac{14}{t^{4}} \hspace{2em} y( -1 )= -2"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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-%203%20%5C,%20%7By%7D%20=%20-%5Cfrac%7B14%7D%7Bt%5E%7B4%7D%7D%20%5Chspace%7B2em%7D%20y(%20-1%20)=%20-2" alt="{y'} t - 3 \, {y} = -\frac{14}{t^{4}} \hspace{2em} y( -1 )= -2" title="{y'} t - 3 \, {y} = -\frac{14}{t^{4}} \hspace{2em} y( -1 )= -2" data-latex="{y'} t - 3 \, {y} = -\frac{14}{t^{4}} \hspace{2em} y( -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?{y} = 4 \, t^{3} + \frac{2}{t^{4}}" alt="{y} = 4 \, t^{3} + \frac{2}{t^{4}}" title="{y} = 4 \, t^{3} + \frac{2}{t^{4}}" data-latex="{y} = 4 \, t^{3} + \frac{2}{t^{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?%7By%7D%20=%204%20%5C,%20t%5E%7B3%7D%20+%20%5Cfrac%7B2%7D%7Bt%5E%7B4%7D%7D" alt="{y} = 4 \, t^{3} + \frac{2}{t^{4}}" title="{y} = 4 \, t^{3} + \frac{2}{t^{4}}" data-latex="{y} = 4 \, t^{3} + \frac{2}{t^{4}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-1576" title="F3 | Techniques for linear IVPs | ver. 1576"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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 + 4 \, {y} = -\frac{18}{t^{2}} \hspace{2em} y( -1 )= -7" alt="-{y'} t + 4 \, {y} = -\frac{18}{t^{2}} \hspace{2em} y( -1 )= -7" title="-{y'} t + 4 \, {y} = -\frac{18}{t^{2}} \hspace{2em} y( -1 )= -7" data-latex="-{y'} t + 4 \, {y} = -\frac{18}{t^{2}} \hspace{2em} y( -1 )= -7"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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+%204%20%5C,%20%7By%7D%20=%20-%5Cfrac%7B18%7D%7Bt%5E%7B2%7D%7D%20%5Chspace%7B2em%7D%20y(%20-1%20)=%20-7" alt="-{y'} t + 4 \, {y} = -\frac{18}{t^{2}} \hspace{2em} y( -1 )= -7" title="-{y'} t + 4 \, {y} = -\frac{18}{t^{2}} \hspace{2em} y( -1 )= -7" data-latex="-{y'} t + 4 \, {y} = -\frac{18}{t^{2}} \hspace{2em} y( -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?{y} = -4 \, t^{4} - \frac{3}{t^{2}}" alt="{y} = -4 \, t^{4} - \frac{3}{t^{2}}" title="{y} = -4 \, t^{4} - \frac{3}{t^{2}}" data-latex="{y} = -4 \, t^{4} - \frac{3}{t^{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?%7By%7D%20=%20-4%20%5C,%20t%5E%7B4%7D%20-%20%5Cfrac%7B3%7D%7Bt%5E%7B2%7D%7D" alt="{y} = -4 \, t^{4} - \frac{3}{t^{2}}" title="{y} = -4 \, t^{4} - \frac{3}{t^{2}}" data-latex="{y} = -4 \, t^{4} - \frac{3}{t^{2}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-5760" title="F3 | Techniques for linear IVPs | ver. 5760"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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?3 \, {y} = -{y'} t + 20 \, t^{2} \hspace{2em} y( -1 )= 6" alt="3 \, {y} = -{y'} t + 20 \, t^{2} \hspace{2em} y( -1 )= 6" title="3 \, {y} = -{y'} t + 20 \, t^{2} \hspace{2em} y( -1 )= 6" data-latex="3 \, {y} = -{y'} t + 20 \, t^{2} \hspace{2em} y( -1 )= 6"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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?3%20%5C,%20%7By%7D%20=%20-%7By'%7D%20t%20+%2020%20%5C,%20t%5E%7B2%7D%20%5Chspace%7B2em%7D%20y(%20-1%20)=%206" alt="3 \, {y} = -{y'} t + 20 \, t^{2} \hspace{2em} y( -1 )= 6" title="3 \, {y} = -{y'} t + 20 \, t^{2} \hspace{2em} y( -1 )= 6" data-latex="3 \, {y} = -{y'} t + 20 \, t^{2} \hspace{2em} y( -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?{y} = 4 \, t^{2} - \frac{2}{t^{3}}" alt="{y} = 4 \, t^{2} - \frac{2}{t^{3}}" title="{y} = 4 \, t^{2} - \frac{2}{t^{3}}" data-latex="{y} = 4 \, t^{2} - \frac{2}{t^{3}}"/></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?%7By%7D%20=%204%20%5C,%20t%5E%7B2%7D%20-%20%5Cfrac%7B2%7D%7Bt%5E%7B3%7D%7D" alt="{y} = 4 \, t^{2} - \frac{2}{t^{3}}" title="{y} = 4 \, t^{2} - \frac{2}{t^{3}}" data-latex="{y} = 4 \, t^{2} - \frac{2}{t^{3}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-7165" title="F3 | Techniques for linear IVPs | ver. 7165"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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 {y'} = -4 \, {y} + \frac{8}{t^{2}} \hspace{2em} y( 1 )= 1" alt="t {y'} = -4 \, {y} + \frac{8}{t^{2}} \hspace{2em} y( 1 )= 1" title="t {y'} = -4 \, {y} + \frac{8}{t^{2}} \hspace{2em} y( 1 )= 1" data-latex="t {y'} = -4 \, {y} + \frac{8}{t^{2}} \hspace{2em} y( 1 )= 1"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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%7By'%7D%20=%20-4%20%5C,%20%7By%7D%20+%20%5Cfrac%7B8%7D%7Bt%5E%7B2%7D%7D%20%5Chspace%7B2em%7D%20y(%201%20)=%201" alt="t {y'} = -4 \, {y} + \frac{8}{t^{2}} \hspace{2em} y( 1 )= 1" title="t {y'} = -4 \, {y} + \frac{8}{t^{2}} \hspace{2em} y( 1 )= 1" data-latex="t {y'} = -4 \, {y} + \frac{8}{t^{2}} \hspace{2em} y( 1 )= 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?{y} = \frac{4}{t^{2}} - \frac{3}{t^{4}}" alt="{y} = \frac{4}{t^{2}} - \frac{3}{t^{4}}" title="{y} = \frac{4}{t^{2}} - \frac{3}{t^{4}}" data-latex="{y} = \frac{4}{t^{2}} - \frac{3}{t^{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?%7By%7D%20=%20%5Cfrac%7B4%7D%7Bt%5E%7B2%7D%7D%20-%20%5Cfrac%7B3%7D%7Bt%5E%7B4%7D%7D" alt="{y} = \frac{4}{t^{2}} - \frac{3}{t^{4}}" title="{y} = \frac{4}{t^{2}} - \frac{3}{t^{4}}" data-latex="{y} = \frac{4}{t^{2}} - \frac{3}{t^{4}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-0945" title="F3 | Techniques for linear IVPs | ver. 0945"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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'} t + 2 \, {y} - \frac{2}{t} \hspace{2em} y( 1 )= 1" alt="0 = {y'} t + 2 \, {y} - \frac{2}{t} \hspace{2em} y( 1 )= 1" title="0 = {y'} t + 2 \, {y} - \frac{2}{t} \hspace{2em} y( 1 )= 1" data-latex="0 = {y'} t + 2 \, {y} - \frac{2}{t} \hspace{2em} y( 1 )= 1"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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%20t%20+%202%20%5C,%20%7By%7D%20-%20%5Cfrac%7B2%7D%7Bt%7D%20%5Chspace%7B2em%7D%20y(%201%20)=%201" alt="0 = {y'} t + 2 \, {y} - \frac{2}{t} \hspace{2em} y( 1 )= 1" title="0 = {y'} t + 2 \, {y} - \frac{2}{t} \hspace{2em} y( 1 )= 1" data-latex="0 = {y'} t + 2 \, {y} - \frac{2}{t} \hspace{2em} y( 1 )= 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?{y} = \frac{2}{t} - \frac{1}{t^{2}}" alt="{y} = \frac{2}{t} - \frac{1}{t^{2}}" title="{y} = \frac{2}{t} - \frac{1}{t^{2}}" data-latex="{y} = \frac{2}{t} - \frac{1}{t^{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?%7By%7D%20=%20%5Cfrac%7B2%7D%7Bt%7D%20-%20%5Cfrac%7B1%7D%7Bt%5E%7B2%7D%7D" alt="{y} = \frac{2}{t} - \frac{1}{t^{2}}" title="{y} = \frac{2}{t} - \frac{1}{t^{2}}" data-latex="{y} = \frac{2}{t} - \frac{1}{t^{2}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-6777" title="F3 | Techniques for linear IVPs | ver. 6777"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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 - 5 \, {y} = \frac{7}{t^{2}} \hspace{2em} y( 1 )= -4" alt="{y'} t - 5 \, {y} = \frac{7}{t^{2}} \hspace{2em} y( 1 )= -4" title="{y'} t - 5 \, {y} = \frac{7}{t^{2}} \hspace{2em} y( 1 )= -4" data-latex="{y'} t - 5 \, {y} = \frac{7}{t^{2}} \hspace{2em} y( 1 )= -4"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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-%205%20%5C,%20%7By%7D%20=%20%5Cfrac%7B7%7D%7Bt%5E%7B2%7D%7D%20%5Chspace%7B2em%7D%20y(%201%20)=%20-4" alt="{y'} t - 5 \, {y} = \frac{7}{t^{2}} \hspace{2em} y( 1 )= -4" title="{y'} t - 5 \, {y} = \frac{7}{t^{2}} \hspace{2em} y( 1 )= -4" data-latex="{y'} t - 5 \, {y} = \frac{7}{t^{2}} \hspace{2em} y( 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?{y} = -3 \, t^{5} - \frac{1}{t^{2}}" alt="{y} = -3 \, t^{5} - \frac{1}{t^{2}}" title="{y} = -3 \, t^{5} - \frac{1}{t^{2}}" data-latex="{y} = -3 \, t^{5} - \frac{1}{t^{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?%7By%7D%20=%20-3%20%5C,%20t%5E%7B5%7D%20-%20%5Cfrac%7B1%7D%7Bt%5E%7B2%7D%7D" alt="{y} = -3 \, t^{5} - \frac{1}{t^{2}}" title="{y} = -3 \, t^{5} - \frac{1}{t^{2}}" data-latex="{y} = -3 \, t^{5} - \frac{1}{t^{2}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-3766" title="F3 | Techniques for linear IVPs | ver. 3766"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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 = -5 \, t^{2} + 3 \, {y} \hspace{2em} y( 1 )= -1" alt="-{y'} t = -5 \, t^{2} + 3 \, {y} \hspace{2em} y( 1 )= -1" title="-{y'} t = -5 \, t^{2} + 3 \, {y} \hspace{2em} y( 1 )= -1" data-latex="-{y'} t = -5 \, t^{2} + 3 \, {y} \hspace{2em} y( 1 )= -1"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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=%20-5%20%5C,%20t%5E%7B2%7D%20+%203%20%5C,%20%7By%7D%20%5Chspace%7B2em%7D%20y(%201%20)=%20-1" alt="-{y'} t = -5 \, t^{2} + 3 \, {y} \hspace{2em} y( 1 )= -1" title="-{y'} t = -5 \, t^{2} + 3 \, {y} \hspace{2em} y( 1 )= -1" data-latex="-{y'} t = -5 \, t^{2} + 3 \, {y} \hspace{2em} y( 1 )= -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?{y} = t^{2} - \frac{2}{t^{3}}" alt="{y} = t^{2} - \frac{2}{t^{3}}" title="{y} = t^{2} - \frac{2}{t^{3}}" data-latex="{y} = t^{2} - \frac{2}{t^{3}}"/></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?%7By%7D%20=%20t%5E%7B2%7D%20-%20%5Cfrac%7B2%7D%7Bt%5E%7B3%7D%7D" alt="{y} = t^{2} - \frac{2}{t^{3}}" title="{y} = t^{2} - \frac{2}{t^{3}}" data-latex="{y} = t^{2} - \frac{2}{t^{3}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-8173" title="F3 | Techniques for linear IVPs | ver. 8173"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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?4 \, {y} = {y'} t - \frac{7}{t^{3}} \hspace{2em} y( -1 )= 0" alt="4 \, {y} = {y'} t - \frac{7}{t^{3}} \hspace{2em} y( -1 )= 0" title="4 \, {y} = {y'} t - \frac{7}{t^{3}} \hspace{2em} y( -1 )= 0" data-latex="4 \, {y} = {y'} t - \frac{7}{t^{3}} \hspace{2em} y( -1 )= 0"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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?4%20%5C,%20%7By%7D%20=%20%7By'%7D%20t%20-%20%5Cfrac%7B7%7D%7Bt%5E%7B3%7D%7D%20%5Chspace%7B2em%7D%20y(%20-1%20)=%200" alt="4 \, {y} = {y'} t - \frac{7}{t^{3}} \hspace{2em} y( -1 )= 0" title="4 \, {y} = {y'} t - \frac{7}{t^{3}} \hspace{2em} y( -1 )= 0" data-latex="4 \, {y} = {y'} t - \frac{7}{t^{3}} \hspace{2em} y( -1 )= 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?{y} = -t^{4} - \frac{1}{t^{3}}" alt="{y} = -t^{4} - \frac{1}{t^{3}}" title="{y} = -t^{4} - \frac{1}{t^{3}}" data-latex="{y} = -t^{4} - \frac{1}{t^{3}}"/></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?%7By%7D%20=%20-t%5E%7B4%7D%20-%20%5Cfrac%7B1%7D%7Bt%5E%7B3%7D%7D" alt="{y} = -t^{4} - \frac{1}{t^{3}}" title="{y} = -t^{4} - \frac{1}{t^{3}}" data-latex="{y} = -t^{4} - \frac{1}{t^{3}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-8576" title="F3 | Techniques for linear IVPs | ver. 8576"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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?-4 \, {y} = -t {y'} + \frac{10}{t} \hspace{2em} y( 1 )= 2" alt="-4 \, {y} = -t {y'} + \frac{10}{t} \hspace{2em} y( 1 )= 2" title="-4 \, {y} = -t {y'} + \frac{10}{t} \hspace{2em} y( 1 )= 2" data-latex="-4 \, {y} = -t {y'} + \frac{10}{t} \hspace{2em} y( 1 )= 2"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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?-4%20%5C,%20%7By%7D%20=%20-t%20%7By'%7D%20+%20%5Cfrac%7B10%7D%7Bt%7D%20%5Chspace%7B2em%7D%20y(%201%20)=%202" alt="-4 \, {y} = -t {y'} + \frac{10}{t} \hspace{2em} y( 1 )= 2" title="-4 \, {y} = -t {y'} + \frac{10}{t} \hspace{2em} y( 1 )= 2" data-latex="-4 \, {y} = -t {y'} + \frac{10}{t} \hspace{2em} y( 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?{y} = 4 \, t^{4} - \frac{2}{t}" alt="{y} = 4 \, t^{4} - \frac{2}{t}" title="{y} = 4 \, t^{4} - \frac{2}{t}" data-latex="{y} = 4 \, t^{4} - \frac{2}{t}"/></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?%7By%7D%20=%204%20%5C,%20t%5E%7B4%7D%20-%20%5Cfrac%7B2%7D%7Bt%7D" alt="{y} = 4 \, t^{4} - \frac{2}{t}" title="{y} = 4 \, t^{4} - \frac{2}{t}" data-latex="{y} = 4 \, t^{4} - \frac{2}{t}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-6070" title="F3 | Techniques for linear IVPs | ver. 6070"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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 {y'} - 4 \, {y} = -\frac{18}{t^{2}} \hspace{2em} y( -1 )= 7" alt="t {y'} - 4 \, {y} = -\frac{18}{t^{2}} \hspace{2em} y( -1 )= 7" title="t {y'} - 4 \, {y} = -\frac{18}{t^{2}} \hspace{2em} y( -1 )= 7" data-latex="t {y'} - 4 \, {y} = -\frac{18}{t^{2}} \hspace{2em} y( -1 )= 7"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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%7By'%7D%20-%204%20%5C,%20%7By%7D%20=%20-%5Cfrac%7B18%7D%7Bt%5E%7B2%7D%7D%20%5Chspace%7B2em%7D%20y(%20-1%20)=%207" alt="t {y'} - 4 \, {y} = -\frac{18}{t^{2}} \hspace{2em} y( -1 )= 7" title="t {y'} - 4 \, {y} = -\frac{18}{t^{2}} \hspace{2em} y( -1 )= 7" data-latex="t {y'} - 4 \, {y} = -\frac{18}{t^{2}} \hspace{2em} y( -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?{y} = 4 \, t^{4} + \frac{3}{t^{2}}" alt="{y} = 4 \, t^{4} + \frac{3}{t^{2}}" title="{y} = 4 \, t^{4} + \frac{3}{t^{2}}" data-latex="{y} = 4 \, t^{4} + \frac{3}{t^{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?%7By%7D%20=%204%20%5C,%20t%5E%7B4%7D%20+%20%5Cfrac%7B3%7D%7Bt%5E%7B2%7D%7D" alt="{y} = 4 \, t^{4} + \frac{3}{t^{2}}" title="{y} = 4 \, t^{4} + \frac{3}{t^{2}}" data-latex="{y} = 4 \, t^{4} + \frac{3}{t^{2}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-7264" title="F3 | Techniques for linear IVPs | ver. 7264"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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 + 4 \, {y} = -2 \, t^{2} \hspace{2em} y( 1 )= -4" alt="-{y'} t + 4 \, {y} = -2 \, t^{2} \hspace{2em} y( 1 )= -4" title="-{y'} t + 4 \, {y} = -2 \, t^{2} \hspace{2em} y( 1 )= -4" data-latex="-{y'} t + 4 \, {y} = -2 \, t^{2} \hspace{2em} y( 1 )= -4"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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+%204%20%5C,%20%7By%7D%20=%20-2%20%5C,%20t%5E%7B2%7D%20%5Chspace%7B2em%7D%20y(%201%20)=%20-4" alt="-{y'} t + 4 \, {y} = -2 \, t^{2} \hspace{2em} y( 1 )= -4" title="-{y'} t + 4 \, {y} = -2 \, t^{2} \hspace{2em} y( 1 )= -4" data-latex="-{y'} t + 4 \, {y} = -2 \, t^{2} \hspace{2em} y( 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?{y} = -3 \, t^{4} - t^{2}" alt="{y} = -3 \, t^{4} - t^{2}" title="{y} = -3 \, t^{4} - t^{2}" data-latex="{y} = -3 \, t^{4} - t^{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?%7By%7D%20=%20-3%20%5C,%20t%5E%7B4%7D%20-%20t%5E%7B2%7D" alt="{y} = -3 \, t^{4} - t^{2}" title="{y} = -3 \, t^{4} - t^{2}" data-latex="{y} = -3 \, t^{4} - t^{2}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-3699" title="F3 | Techniques for linear IVPs | ver. 3699"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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?10 \, t^{3} - 5 \, {y} = -{y'} t \hspace{2em} y( 1 )= 4" alt="10 \, t^{3} - 5 \, {y} = -{y'} t \hspace{2em} y( 1 )= 4" title="10 \, t^{3} - 5 \, {y} = -{y'} t \hspace{2em} y( 1 )= 4" data-latex="10 \, t^{3} - 5 \, {y} = -{y'} t \hspace{2em} y( 1 )= 4"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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?10%20%5C,%20t%5E%7B3%7D%20-%205%20%5C,%20%7By%7D%20=%20-%7By'%7D%20t%20%5Chspace%7B2em%7D%20y(%201%20)=%204" alt="10 \, t^{3} - 5 \, {y} = -{y'} t \hspace{2em} y( 1 )= 4" title="10 \, t^{3} - 5 \, {y} = -{y'} t \hspace{2em} y( 1 )= 4" data-latex="10 \, t^{3} - 5 \, {y} = -{y'} t \hspace{2em} y( 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?{y} = -t^{5} + 5 \, t^{3}" alt="{y} = -t^{5} + 5 \, t^{3}" title="{y} = -t^{5} + 5 \, t^{3}" data-latex="{y} = -t^{5} + 5 \, t^{3}"/></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?%7By%7D%20=%20-t%5E%7B5%7D%20+%205%20%5C,%20t%5E%7B3%7D" alt="{y} = -t^{5} + 5 \, t^{3}" title="{y} = -t^{5} + 5 \, t^{3}" data-latex="{y} = -t^{5} + 5 \, t^{3}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-5817" title="F3 | Techniques for linear IVPs | ver. 5817"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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?-\frac{20}{t} = -{y'} t - 5 \, {y} \hspace{2em} y( 1 )= 8" alt="-\frac{20}{t} = -{y'} t - 5 \, {y} \hspace{2em} y( 1 )= 8" title="-\frac{20}{t} = -{y'} t - 5 \, {y} \hspace{2em} y( 1 )= 8" data-latex="-\frac{20}{t} = -{y'} t - 5 \, {y} \hspace{2em} y( 1 )= 8"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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?-%5Cfrac%7B20%7D%7Bt%7D%20=%20-%7By'%7D%20t%20-%205%20%5C,%20%7By%7D%20%5Chspace%7B2em%7D%20y(%201%20)=%208" alt="-\frac{20}{t} = -{y'} t - 5 \, {y} \hspace{2em} y( 1 )= 8" title="-\frac{20}{t} = -{y'} t - 5 \, {y} \hspace{2em} y( 1 )= 8" data-latex="-\frac{20}{t} = -{y'} t - 5 \, {y} \hspace{2em} y( 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?{y} = \frac{5}{t} + \frac{3}{t^{5}}" alt="{y} = \frac{5}{t} + \frac{3}{t^{5}}" title="{y} = \frac{5}{t} + \frac{3}{t^{5}}" data-latex="{y} = \frac{5}{t} + \frac{3}{t^{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?%7By%7D%20=%20%5Cfrac%7B5%7D%7Bt%7D%20+%20%5Cfrac%7B3%7D%7Bt%5E%7B5%7D%7D" alt="{y} = \frac{5}{t} + \frac{3}{t^{5}}" title="{y} = \frac{5}{t} + \frac{3}{t^{5}}" data-latex="{y} = \frac{5}{t} + \frac{3}{t^{5}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-5960" title="F3 | Techniques for linear IVPs | ver. 5960"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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'} t - 2 \, {y} + \frac{3}{t^{3}} \hspace{2em} y( -1 )= 5" alt="0 = -{y'} t - 2 \, {y} + \frac{3}{t^{3}} \hspace{2em} y( -1 )= 5" title="0 = -{y'} t - 2 \, {y} + \frac{3}{t^{3}} \hspace{2em} y( -1 )= 5" data-latex="0 = -{y'} t - 2 \, {y} + \frac{3}{t^{3}} \hspace{2em} y( -1 )= 5"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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%20t%20-%202%20%5C,%20%7By%7D%20+%20%5Cfrac%7B3%7D%7Bt%5E%7B3%7D%7D%20%5Chspace%7B2em%7D%20y(%20-1%20)=%205" alt="0 = -{y'} t - 2 \, {y} + \frac{3}{t^{3}} \hspace{2em} y( -1 )= 5" title="0 = -{y'} t - 2 \, {y} + \frac{3}{t^{3}} \hspace{2em} y( -1 )= 5" data-latex="0 = -{y'} t - 2 \, {y} + \frac{3}{t^{3}} \hspace{2em} y( -1 )= 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?{y} = \frac{2}{t^{2}} - \frac{3}{t^{3}}" alt="{y} = \frac{2}{t^{2}} - \frac{3}{t^{3}}" title="{y} = \frac{2}{t^{2}} - \frac{3}{t^{3}}" data-latex="{y} = \frac{2}{t^{2}} - \frac{3}{t^{3}}"/></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?%7By%7D%20=%20%5Cfrac%7B2%7D%7Bt%5E%7B2%7D%7D%20-%20%5Cfrac%7B3%7D%7Bt%5E%7B3%7D%7D" alt="{y} = \frac{2}{t^{2}} - \frac{3}{t^{3}}" title="{y} = \frac{2}{t^{2}} - \frac{3}{t^{3}}" data-latex="{y} = \frac{2}{t^{2}} - \frac{3}{t^{3}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-7378" title="F3 | Techniques for linear IVPs | ver. 7378"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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?-\frac{6}{t} = -t {y'} + 5 \, {y} \hspace{2em} y( 1 )= -5" alt="-\frac{6}{t} = -t {y'} + 5 \, {y} \hspace{2em} y( 1 )= -5" title="-\frac{6}{t} = -t {y'} + 5 \, {y} \hspace{2em} y( 1 )= -5" data-latex="-\frac{6}{t} = -t {y'} + 5 \, {y} \hspace{2em} y( 1 )= -5"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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?-%5Cfrac%7B6%7D%7Bt%7D%20=%20-t%20%7By'%7D%20+%205%20%5C,%20%7By%7D%20%5Chspace%7B2em%7D%20y(%201%20)=%20-5" alt="-\frac{6}{t} = -t {y'} + 5 \, {y} \hspace{2em} y( 1 )= -5" title="-\frac{6}{t} = -t {y'} + 5 \, {y} \hspace{2em} y( 1 )= -5" data-latex="-\frac{6}{t} = -t {y'} + 5 \, {y} \hspace{2em} y( 1 )= -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?{y} = -4 \, t^{5} - \frac{1}{t}" alt="{y} = -4 \, t^{5} - \frac{1}{t}" title="{y} = -4 \, t^{5} - \frac{1}{t}" data-latex="{y} = -4 \, t^{5} - \frac{1}{t}"/></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?%7By%7D%20=%20-4%20%5C,%20t%5E%7B5%7D%20-%20%5Cfrac%7B1%7D%7Bt%7D" alt="{y} = -4 \, t^{5} - \frac{1}{t}" title="{y} = -4 \, t^{5} - \frac{1}{t}" data-latex="{y} = -4 \, t^{5} - \frac{1}{t}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-9381" title="F3 | Techniques for linear IVPs | ver. 9381"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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 {y'} = 3 \, {y} - \frac{12}{t} \hspace{2em} y( 1 )= 7" alt="t {y'} = 3 \, {y} - \frac{12}{t} \hspace{2em} y( 1 )= 7" title="t {y'} = 3 \, {y} - \frac{12}{t} \hspace{2em} y( 1 )= 7" data-latex="t {y'} = 3 \, {y} - \frac{12}{t} \hspace{2em} y( 1 )= 7"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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%7By'%7D%20=%203%20%5C,%20%7By%7D%20-%20%5Cfrac%7B12%7D%7Bt%7D%20%5Chspace%7B2em%7D%20y(%201%20)=%207" alt="t {y'} = 3 \, {y} - \frac{12}{t} \hspace{2em} y( 1 )= 7" title="t {y'} = 3 \, {y} - \frac{12}{t} \hspace{2em} y( 1 )= 7" data-latex="t {y'} = 3 \, {y} - \frac{12}{t} \hspace{2em} y( 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?{y} = 4 \, t^{3} + \frac{3}{t}" alt="{y} = 4 \, t^{3} + \frac{3}{t}" title="{y} = 4 \, t^{3} + \frac{3}{t}" data-latex="{y} = 4 \, t^{3} + \frac{3}{t}"/></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?%7By%7D%20=%204%20%5C,%20t%5E%7B3%7D%20+%20%5Cfrac%7B3%7D%7Bt%7D" alt="{y} = 4 \, t^{3} + \frac{3}{t}" title="{y} = 4 \, t^{3} + \frac{3}{t}" data-latex="{y} = 4 \, t^{3} + \frac{3}{t}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-4868" title="F3 | Techniques for linear IVPs | ver. 4868"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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?5 \, t = {y'} t - 2 \, {y} \hspace{2em} y( 1 )= -4" alt="5 \, t = {y'} t - 2 \, {y} \hspace{2em} y( 1 )= -4" title="5 \, t = {y'} t - 2 \, {y} \hspace{2em} y( 1 )= -4" data-latex="5 \, t = {y'} t - 2 \, {y} \hspace{2em} y( 1 )= -4"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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?5%20%5C,%20t%20=%20%7By'%7D%20t%20-%202%20%5C,%20%7By%7D%20%5Chspace%7B2em%7D%20y(%201%20)=%20-4" alt="5 \, t = {y'} t - 2 \, {y} \hspace{2em} y( 1 )= -4" title="5 \, t = {y'} t - 2 \, {y} \hspace{2em} y( 1 )= -4" data-latex="5 \, t = {y'} t - 2 \, {y} \hspace{2em} y( 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?{y} = t^{2} - 5 \, t" alt="{y} = t^{2} - 5 \, t" title="{y} = t^{2} - 5 \, t" data-latex="{y} = t^{2} - 5 \, t"/></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?%7By%7D%20=%20t%5E%7B2%7D%20-%205%20%5C,%20t" alt="{y} = t^{2} - 5 \, t" title="{y} = t^{2} - 5 \, t" data-latex="{y} = t^{2} - 5 \, t"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-5561" title="F3 | Techniques for linear IVPs | ver. 5561"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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?-4 \, {y} - \frac{6}{t} = {y'} t \hspace{2em} y( -1 )= 1" alt="-4 \, {y} - \frac{6}{t} = {y'} t \hspace{2em} y( -1 )= 1" title="-4 \, {y} - \frac{6}{t} = {y'} t \hspace{2em} y( -1 )= 1" data-latex="-4 \, {y} - \frac{6}{t} = {y'} t \hspace{2em} y( -1 )= 1"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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?-4%20%5C,%20%7By%7D%20-%20%5Cfrac%7B6%7D%7Bt%7D%20=%20%7By'%7D%20t%20%5Chspace%7B2em%7D%20y(%20-1%20)=%201" alt="-4 \, {y} - \frac{6}{t} = {y'} t \hspace{2em} y( -1 )= 1" title="-4 \, {y} - \frac{6}{t} = {y'} t \hspace{2em} y( -1 )= 1" data-latex="-4 \, {y} - \frac{6}{t} = {y'} t \hspace{2em} y( -1 )= 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?{y} = -\frac{2}{t} - \frac{1}{t^{4}}" alt="{y} = -\frac{2}{t} - \frac{1}{t^{4}}" title="{y} = -\frac{2}{t} - \frac{1}{t^{4}}" data-latex="{y} = -\frac{2}{t} - \frac{1}{t^{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?%7By%7D%20=%20-%5Cfrac%7B2%7D%7Bt%7D%20-%20%5Cfrac%7B1%7D%7Bt%5E%7B4%7D%7D" alt="{y} = -\frac{2}{t} - \frac{1}{t^{4}}" title="{y} = -\frac{2}{t} - \frac{1}{t^{4}}" data-latex="{y} = -\frac{2}{t} - \frac{1}{t^{4}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-4769" title="F3 | Techniques for linear IVPs | ver. 4769"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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} + t {y'} - 3 \, {y} = 0 \hspace{2em} y( -1 )= -1" alt="t^{2} + t {y'} - 3 \, {y} = 0 \hspace{2em} y( -1 )= -1" title="t^{2} + t {y'} - 3 \, {y} = 0 \hspace{2em} y( -1 )= -1" data-latex="t^{2} + t {y'} - 3 \, {y} = 0 \hspace{2em} y( -1 )= -1"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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+%20t%20%7By'%7D%20-%203%20%5C,%20%7By%7D%20=%200%20%5Chspace%7B2em%7D%20y(%20-1%20)=%20-1" alt="t^{2} + t {y'} - 3 \, {y} = 0 \hspace{2em} y( -1 )= -1" title="t^{2} + t {y'} - 3 \, {y} = 0 \hspace{2em} y( -1 )= -1" data-latex="t^{2} + t {y'} - 3 \, {y} = 0 \hspace{2em} y( -1 )= -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?{y} = 2 \, t^{3} + t^{2}" alt="{y} = 2 \, t^{3} + t^{2}" title="{y} = 2 \, t^{3} + t^{2}" data-latex="{y} = 2 \, t^{3} + t^{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?%7By%7D%20=%202%20%5C,%20t%5E%7B3%7D%20+%20t%5E%7B2%7D" alt="{y} = 2 \, t^{3} + t^{2}" title="{y} = 2 \, t^{3} + t^{2}" data-latex="{y} = 2 \, t^{3} + t^{2}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-2729" title="F3 | Techniques for linear IVPs | ver. 2729"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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 + 4 \, {y} = -15 \, t \hspace{2em} y( 1 )= -1" alt="{y'} t + 4 \, {y} = -15 \, t \hspace{2em} y( 1 )= -1" title="{y'} t + 4 \, {y} = -15 \, t \hspace{2em} y( 1 )= -1" data-latex="{y'} t + 4 \, {y} = -15 \, t \hspace{2em} y( 1 )= -1"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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+%204%20%5C,%20%7By%7D%20=%20-15%20%5C,%20t%20%5Chspace%7B2em%7D%20y(%201%20)=%20-1" alt="{y'} t + 4 \, {y} = -15 \, t \hspace{2em} y( 1 )= -1" title="{y'} t + 4 \, {y} = -15 \, t \hspace{2em} y( 1 )= -1" data-latex="{y'} t + 4 \, {y} = -15 \, t \hspace{2em} y( 1 )= -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?{y} = -3 \, t + \frac{2}{t^{4}}" alt="{y} = -3 \, t + \frac{2}{t^{4}}" title="{y} = -3 \, t + \frac{2}{t^{4}}" data-latex="{y} = -3 \, t + \frac{2}{t^{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?%7By%7D%20=%20-3%20%5C,%20t%20+%20%5Cfrac%7B2%7D%7Bt%5E%7B4%7D%7D" alt="{y} = -3 \, t + \frac{2}{t^{4}}" title="{y} = -3 \, t + \frac{2}{t^{4}}" data-latex="{y} = -3 \, t + \frac{2}{t^{4}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-6733" title="F3 | Techniques for linear IVPs | ver. 6733"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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?-4 \, {y} = t {y'} + \frac{1}{t^{3}} \hspace{2em} y( 1 )= -5" alt="-4 \, {y} = t {y'} + \frac{1}{t^{3}} \hspace{2em} y( 1 )= -5" title="-4 \, {y} = t {y'} + \frac{1}{t^{3}} \hspace{2em} y( 1 )= -5" data-latex="-4 \, {y} = t {y'} + \frac{1}{t^{3}} \hspace{2em} y( 1 )= -5"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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?-4%20%5C,%20%7By%7D%20=%20t%20%7By'%7D%20+%20%5Cfrac%7B1%7D%7Bt%5E%7B3%7D%7D%20%5Chspace%7B2em%7D%20y(%201%20)=%20-5" alt="-4 \, {y} = t {y'} + \frac{1}{t^{3}} \hspace{2em} y( 1 )= -5" title="-4 \, {y} = t {y'} + \frac{1}{t^{3}} \hspace{2em} y( 1 )= -5" data-latex="-4 \, {y} = t {y'} + \frac{1}{t^{3}} \hspace{2em} y( 1 )= -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?{y} = -\frac{1}{t^{3}} - \frac{4}{t^{4}}" alt="{y} = -\frac{1}{t^{3}} - \frac{4}{t^{4}}" title="{y} = -\frac{1}{t^{3}} - \frac{4}{t^{4}}" data-latex="{y} = -\frac{1}{t^{3}} - \frac{4}{t^{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?%7By%7D%20=%20-%5Cfrac%7B1%7D%7Bt%5E%7B3%7D%7D%20-%20%5Cfrac%7B4%7D%7Bt%5E%7B4%7D%7D" alt="{y} = -\frac{1}{t^{3}} - \frac{4}{t^{4}}" title="{y} = -\frac{1}{t^{3}} - \frac{4}{t^{4}}" data-latex="{y} = -\frac{1}{t^{3}} - \frac{4}{t^{4}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-3015" title="F3 | Techniques for linear IVPs | ver. 3015"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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'} t - 5 \, {y} - \frac{9}{t^{2}} \hspace{2em} y( 1 )= 1" alt="0 = -{y'} t - 5 \, {y} - \frac{9}{t^{2}} \hspace{2em} y( 1 )= 1" title="0 = -{y'} t - 5 \, {y} - \frac{9}{t^{2}} \hspace{2em} y( 1 )= 1" data-latex="0 = -{y'} t - 5 \, {y} - \frac{9}{t^{2}} \hspace{2em} y( 1 )= 1"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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%20t%20-%205%20%5C,%20%7By%7D%20-%20%5Cfrac%7B9%7D%7Bt%5E%7B2%7D%7D%20%5Chspace%7B2em%7D%20y(%201%20)=%201" alt="0 = -{y'} t - 5 \, {y} - \frac{9}{t^{2}} \hspace{2em} y( 1 )= 1" title="0 = -{y'} t - 5 \, {y} - \frac{9}{t^{2}} \hspace{2em} y( 1 )= 1" data-latex="0 = -{y'} t - 5 \, {y} - \frac{9}{t^{2}} \hspace{2em} y( 1 )= 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?{y} = -\frac{3}{t^{2}} + \frac{4}{t^{5}}" alt="{y} = -\frac{3}{t^{2}} + \frac{4}{t^{5}}" title="{y} = -\frac{3}{t^{2}} + \frac{4}{t^{5}}" data-latex="{y} = -\frac{3}{t^{2}} + \frac{4}{t^{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?%7By%7D%20=%20-%5Cfrac%7B3%7D%7Bt%5E%7B2%7D%7D%20+%20%5Cfrac%7B4%7D%7Bt%5E%7B5%7D%7D" alt="{y} = -\frac{3}{t^{2}} + \frac{4}{t^{5}}" title="{y} = -\frac{3}{t^{2}} + \frac{4}{t^{5}}" data-latex="{y} = -\frac{3}{t^{2}} + \frac{4}{t^{5}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-8137" title="F3 | Techniques for linear IVPs | ver. 8137"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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?-2 \, {y} - \frac{3}{t} = -{y'} t \hspace{2em} y( 1 )= -5" alt="-2 \, {y} - \frac{3}{t} = -{y'} t \hspace{2em} y( 1 )= -5" title="-2 \, {y} - \frac{3}{t} = -{y'} t \hspace{2em} y( 1 )= -5" data-latex="-2 \, {y} - \frac{3}{t} = -{y'} t \hspace{2em} y( 1 )= -5"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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?-2%20%5C,%20%7By%7D%20-%20%5Cfrac%7B3%7D%7Bt%7D%20=%20-%7By'%7D%20t%20%5Chspace%7B2em%7D%20y(%201%20)=%20-5" alt="-2 \, {y} - \frac{3}{t} = -{y'} t \hspace{2em} y( 1 )= -5" title="-2 \, {y} - \frac{3}{t} = -{y'} t \hspace{2em} y( 1 )= -5" data-latex="-2 \, {y} - \frac{3}{t} = -{y'} t \hspace{2em} y( 1 )= -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?{y} = -4 \, t^{2} - \frac{1}{t}" alt="{y} = -4 \, t^{2} - \frac{1}{t}" title="{y} = -4 \, t^{2} - \frac{1}{t}" data-latex="{y} = -4 \, t^{2} - \frac{1}{t}"/></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?%7By%7D%20=%20-4%20%5C,%20t%5E%7B2%7D%20-%20%5Cfrac%7B1%7D%7Bt%7D" alt="{y} = -4 \, t^{2} - \frac{1}{t}" title="{y} = -4 \, t^{2} - \frac{1}{t}" data-latex="{y} = -4 \, t^{2} - \frac{1}{t}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-3369" title="F3 | Techniques for linear IVPs | ver. 3369"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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'} t - 3 \, {y} - \frac{1}{t^{4}} \hspace{2em} y( 1 )= 3" alt="0 = -{y'} t - 3 \, {y} - \frac{1}{t^{4}} \hspace{2em} y( 1 )= 3" title="0 = -{y'} t - 3 \, {y} - \frac{1}{t^{4}} \hspace{2em} y( 1 )= 3" data-latex="0 = -{y'} t - 3 \, {y} - \frac{1}{t^{4}} \hspace{2em} y( 1 )= 3"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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%20t%20-%203%20%5C,%20%7By%7D%20-%20%5Cfrac%7B1%7D%7Bt%5E%7B4%7D%7D%20%5Chspace%7B2em%7D%20y(%201%20)=%203" alt="0 = -{y'} t - 3 \, {y} - \frac{1}{t^{4}} \hspace{2em} y( 1 )= 3" title="0 = -{y'} t - 3 \, {y} - \frac{1}{t^{4}} \hspace{2em} y( 1 )= 3" data-latex="0 = -{y'} t - 3 \, {y} - \frac{1}{t^{4}} \hspace{2em} y( 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?{y} = \frac{2}{t^{3}} + \frac{1}{t^{4}}" alt="{y} = \frac{2}{t^{3}} + \frac{1}{t^{4}}" title="{y} = \frac{2}{t^{3}} + \frac{1}{t^{4}}" data-latex="{y} = \frac{2}{t^{3}} + \frac{1}{t^{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?%7By%7D%20=%20%5Cfrac%7B2%7D%7Bt%5E%7B3%7D%7D%20+%20%5Cfrac%7B1%7D%7Bt%5E%7B4%7D%7D" alt="{y} = \frac{2}{t^{3}} + \frac{1}{t^{4}}" title="{y} = \frac{2}{t^{3}} + \frac{1}{t^{4}}" data-latex="{y} = \frac{2}{t^{3}} + \frac{1}{t^{4}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-4144" title="F3 | Techniques for linear IVPs | ver. 4144"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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'} t + 2 \, {y} + 15 \, t \hspace{2em} y( 1 )= -9" alt="0 = {y'} t + 2 \, {y} + 15 \, t \hspace{2em} y( 1 )= -9" title="0 = {y'} t + 2 \, {y} + 15 \, t \hspace{2em} y( 1 )= -9" data-latex="0 = {y'} t + 2 \, {y} + 15 \, t \hspace{2em} y( 1 )= -9"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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%20t%20+%202%20%5C,%20%7By%7D%20+%2015%20%5C,%20t%20%5Chspace%7B2em%7D%20y(%201%20)=%20-9" alt="0 = {y'} t + 2 \, {y} + 15 \, t \hspace{2em} y( 1 )= -9" title="0 = {y'} t + 2 \, {y} + 15 \, t \hspace{2em} y( 1 )= -9" data-latex="0 = {y'} t + 2 \, {y} + 15 \, t \hspace{2em} y( 1 )= -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?{y} = -5 \, t - \frac{4}{t^{2}}" alt="{y} = -5 \, t - \frac{4}{t^{2}}" title="{y} = -5 \, t - \frac{4}{t^{2}}" data-latex="{y} = -5 \, t - \frac{4}{t^{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?%7By%7D%20=%20-5%20%5C,%20t%20-%20%5Cfrac%7B4%7D%7Bt%5E%7B2%7D%7D" alt="{y} = -5 \, t - \frac{4}{t^{2}}" title="{y} = -5 \, t - \frac{4}{t^{2}}" data-latex="{y} = -5 \, t - \frac{4}{t^{2}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-8108" title="F3 | Techniques for linear IVPs | ver. 8108"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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'} t + 3 \, {y} - \frac{20}{t^{2}} \hspace{2em} y( -1 )= 2" alt="0 = -{y'} t + 3 \, {y} - \frac{20}{t^{2}} \hspace{2em} y( -1 )= 2" title="0 = -{y'} t + 3 \, {y} - \frac{20}{t^{2}} \hspace{2em} y( -1 )= 2" data-latex="0 = -{y'} t + 3 \, {y} - \frac{20}{t^{2}} \hspace{2em} y( -1 )= 2"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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%20t%20+%203%20%5C,%20%7By%7D%20-%20%5Cfrac%7B20%7D%7Bt%5E%7B2%7D%7D%20%5Chspace%7B2em%7D%20y(%20-1%20)=%202" alt="0 = -{y'} t + 3 \, {y} - \frac{20}{t^{2}} \hspace{2em} y( -1 )= 2" title="0 = -{y'} t + 3 \, {y} - \frac{20}{t^{2}} \hspace{2em} y( -1 )= 2" data-latex="0 = -{y'} t + 3 \, {y} - \frac{20}{t^{2}} \hspace{2em} y( -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?{y} = 2 \, t^{3} + \frac{4}{t^{2}}" alt="{y} = 2 \, t^{3} + \frac{4}{t^{2}}" title="{y} = 2 \, t^{3} + \frac{4}{t^{2}}" data-latex="{y} = 2 \, t^{3} + \frac{4}{t^{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?%7By%7D%20=%202%20%5C,%20t%5E%7B3%7D%20+%20%5Cfrac%7B4%7D%7Bt%5E%7B2%7D%7D" alt="{y} = 2 \, t^{3} + \frac{4}{t^{2}}" title="{y} = 2 \, t^{3} + \frac{4}{t^{2}}" data-latex="{y} = 2 \, t^{3} + \frac{4}{t^{2}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-8978" title="F3 | Techniques for linear IVPs | ver. 8978"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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?-5 \, {y} + \frac{5}{t^{4}} = t {y'} \hspace{2em} y( 1 )= 4" alt="-5 \, {y} + \frac{5}{t^{4}} = t {y'} \hspace{2em} y( 1 )= 4" title="-5 \, {y} + \frac{5}{t^{4}} = t {y'} \hspace{2em} y( 1 )= 4" data-latex="-5 \, {y} + \frac{5}{t^{4}} = t {y'} \hspace{2em} y( 1 )= 4"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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?-5%20%5C,%20%7By%7D%20+%20%5Cfrac%7B5%7D%7Bt%5E%7B4%7D%7D%20=%20t%20%7By'%7D%20%5Chspace%7B2em%7D%20y(%201%20)=%204" alt="-5 \, {y} + \frac{5}{t^{4}} = t {y'} \hspace{2em} y( 1 )= 4" title="-5 \, {y} + \frac{5}{t^{4}} = t {y'} \hspace{2em} y( 1 )= 4" data-latex="-5 \, {y} + \frac{5}{t^{4}} = t {y'} \hspace{2em} y( 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?{y} = \frac{5}{t^{4}} - \frac{1}{t^{5}}" alt="{y} = \frac{5}{t^{4}} - \frac{1}{t^{5}}" title="{y} = \frac{5}{t^{4}} - \frac{1}{t^{5}}" data-latex="{y} = \frac{5}{t^{4}} - \frac{1}{t^{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?%7By%7D%20=%20%5Cfrac%7B5%7D%7Bt%5E%7B4%7D%7D%20-%20%5Cfrac%7B1%7D%7Bt%5E%7B5%7D%7D" alt="{y} = \frac{5}{t^{4}} - \frac{1}{t^{5}}" title="{y} = \frac{5}{t^{4}} - \frac{1}{t^{5}}" data-latex="{y} = \frac{5}{t^{4}} - \frac{1}{t^{5}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-3467" title="F3 | Techniques for linear IVPs | ver. 3467"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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'} t + 5 \, {y} - \frac{3}{t^{4}} \hspace{2em} y( -1 )= 7" alt="0 = {y'} t + 5 \, {y} - \frac{3}{t^{4}} \hspace{2em} y( -1 )= 7" title="0 = {y'} t + 5 \, {y} - \frac{3}{t^{4}} \hspace{2em} y( -1 )= 7" data-latex="0 = {y'} t + 5 \, {y} - \frac{3}{t^{4}} \hspace{2em} y( -1 )= 7"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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%20t%20+%205%20%5C,%20%7By%7D%20-%20%5Cfrac%7B3%7D%7Bt%5E%7B4%7D%7D%20%5Chspace%7B2em%7D%20y(%20-1%20)=%207" alt="0 = {y'} t + 5 \, {y} - \frac{3}{t^{4}} \hspace{2em} y( -1 )= 7" title="0 = {y'} t + 5 \, {y} - \frac{3}{t^{4}} \hspace{2em} y( -1 )= 7" data-latex="0 = {y'} t + 5 \, {y} - \frac{3}{t^{4}} \hspace{2em} y( -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?{y} = \frac{3}{t^{4}} - \frac{4}{t^{5}}" alt="{y} = \frac{3}{t^{4}} - \frac{4}{t^{5}}" title="{y} = \frac{3}{t^{4}} - \frac{4}{t^{5}}" data-latex="{y} = \frac{3}{t^{4}} - \frac{4}{t^{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?%7By%7D%20=%20%5Cfrac%7B3%7D%7Bt%5E%7B4%7D%7D%20-%20%5Cfrac%7B4%7D%7Bt%5E%7B5%7D%7D" alt="{y} = \frac{3}{t^{4}} - \frac{4}{t^{5}}" title="{y} = \frac{3}{t^{4}} - \frac{4}{t^{5}}" data-latex="{y} = \frac{3}{t^{4}} - \frac{4}{t^{5}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-0555" title="F3 | Techniques for linear IVPs | ver. 0555"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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 {y'} + \frac{16}{t^{2}} = -2 \, {y} \hspace{2em} y( -1 )= -5" alt="-t {y'} + \frac{16}{t^{2}} = -2 \, {y} \hspace{2em} y( -1 )= -5" title="-t {y'} + \frac{16}{t^{2}} = -2 \, {y} \hspace{2em} y( -1 )= -5" data-latex="-t {y'} + \frac{16}{t^{2}} = -2 \, {y} \hspace{2em} y( -1 )= -5"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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%7By'%7D%20+%20%5Cfrac%7B16%7D%7Bt%5E%7B2%7D%7D%20=%20-2%20%5C,%20%7By%7D%20%5Chspace%7B2em%7D%20y(%20-1%20)=%20-5" alt="-t {y'} + \frac{16}{t^{2}} = -2 \, {y} \hspace{2em} y( -1 )= -5" title="-t {y'} + \frac{16}{t^{2}} = -2 \, {y} \hspace{2em} y( -1 )= -5" data-latex="-t {y'} + \frac{16}{t^{2}} = -2 \, {y} \hspace{2em} y( -1 )= -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?{y} = -t^{2} - \frac{4}{t^{2}}" alt="{y} = -t^{2} - \frac{4}{t^{2}}" title="{y} = -t^{2} - \frac{4}{t^{2}}" data-latex="{y} = -t^{2} - \frac{4}{t^{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?%7By%7D%20=%20-t%5E%7B2%7D%20-%20%5Cfrac%7B4%7D%7Bt%5E%7B2%7D%7D" alt="{y} = -t^{2} - \frac{4}{t^{2}}" title="{y} = -t^{2} - \frac{4}{t^{2}}" data-latex="{y} = -t^{2} - \frac{4}{t^{2}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-2347" title="F3 | Techniques for linear IVPs | ver. 2347"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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 - \frac{35}{t^{2}} = 5 \, {y} \hspace{2em} y( 1 )= -3" alt="{y'} t - \frac{35}{t^{2}} = 5 \, {y} \hspace{2em} y( 1 )= -3" title="{y'} t - \frac{35}{t^{2}} = 5 \, {y} \hspace{2em} y( 1 )= -3" data-latex="{y'} t - \frac{35}{t^{2}} = 5 \, {y} \hspace{2em} y( 1 )= -3"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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%5Cfrac%7B35%7D%7Bt%5E%7B2%7D%7D%20=%205%20%5C,%20%7By%7D%20%5Chspace%7B2em%7D%20y(%201%20)=%20-3" alt="{y'} t - \frac{35}{t^{2}} = 5 \, {y} \hspace{2em} y( 1 )= -3" title="{y'} t - \frac{35}{t^{2}} = 5 \, {y} \hspace{2em} y( 1 )= -3" data-latex="{y'} t - \frac{35}{t^{2}} = 5 \, {y} \hspace{2em} y( 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?{y} = 2 \, t^{5} - \frac{5}{t^{2}}" alt="{y} = 2 \, t^{5} - \frac{5}{t^{2}}" title="{y} = 2 \, t^{5} - \frac{5}{t^{2}}" data-latex="{y} = 2 \, t^{5} - \frac{5}{t^{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?%7By%7D%20=%202%20%5C,%20t%5E%7B5%7D%20-%20%5Cfrac%7B5%7D%7Bt%5E%7B2%7D%7D" alt="{y} = 2 \, t^{5} - \frac{5}{t^{2}}" title="{y} = 2 \, t^{5} - \frac{5}{t^{2}}" data-latex="{y} = 2 \, t^{5} - \frac{5}{t^{2}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-9044" title="F3 | Techniques for linear IVPs | ver. 9044"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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?-4 \, t^{4} + {y'} t = 3 \, {y} \hspace{2em} y( 1 )= 1" alt="-4 \, t^{4} + {y'} t = 3 \, {y} \hspace{2em} y( 1 )= 1" title="-4 \, t^{4} + {y'} t = 3 \, {y} \hspace{2em} y( 1 )= 1" data-latex="-4 \, t^{4} + {y'} t = 3 \, {y} \hspace{2em} y( 1 )= 1"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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?-4%20%5C,%20t%5E%7B4%7D%20+%20%7By'%7D%20t%20=%203%20%5C,%20%7By%7D%20%5Chspace%7B2em%7D%20y(%201%20)=%201" alt="-4 \, t^{4} + {y'} t = 3 \, {y} \hspace{2em} y( 1 )= 1" title="-4 \, t^{4} + {y'} t = 3 \, {y} \hspace{2em} y( 1 )= 1" data-latex="-4 \, t^{4} + {y'} t = 3 \, {y} \hspace{2em} y( 1 )= 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?{y} = 4 \, t^{4} - 3 \, t^{3}" alt="{y} = 4 \, t^{4} - 3 \, t^{3}" title="{y} = 4 \, t^{4} - 3 \, t^{3}" data-latex="{y} = 4 \, t^{4} - 3 \, t^{3}"/></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?%7By%7D%20=%204%20%5C,%20t%5E%7B4%7D%20-%203%20%5C,%20t%5E%7B3%7D" alt="{y} = 4 \, t^{4} - 3 \, t^{3}" title="{y} = 4 \, t^{4} - 3 \, t^{3}" data-latex="{y} = 4 \, t^{4} - 3 \, t^{3}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-1556" title="F3 | Techniques for linear IVPs | ver. 1556"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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} - 3 \, {y} = -t {y'} \hspace{2em} y( -1 )= -4" alt="t^{4} - 3 \, {y} = -t {y'} \hspace{2em} y( -1 )= -4" title="t^{4} - 3 \, {y} = -t {y'} \hspace{2em} y( -1 )= -4" data-latex="t^{4} - 3 \, {y} = -t {y'} \hspace{2em} y( -1 )= -4"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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%7B4%7D%20-%203%20%5C,%20%7By%7D%20=%20-t%20%7By'%7D%20%5Chspace%7B2em%7D%20y(%20-1%20)=%20-4" alt="t^{4} - 3 \, {y} = -t {y'} \hspace{2em} y( -1 )= -4" title="t^{4} - 3 \, {y} = -t {y'} \hspace{2em} y( -1 )= -4" data-latex="t^{4} - 3 \, {y} = -t {y'} \hspace{2em} y( -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?{y} = -t^{4} + 3 \, t^{3}" alt="{y} = -t^{4} + 3 \, t^{3}" title="{y} = -t^{4} + 3 \, t^{3}" data-latex="{y} = -t^{4} + 3 \, t^{3}"/></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?%7By%7D%20=%20-t%5E%7B4%7D%20+%203%20%5C,%20t%5E%7B3%7D" alt="{y} = -t^{4} + 3 \, t^{3}" title="{y} = -t^{4} + 3 \, t^{3}" data-latex="{y} = -t^{4} + 3 \, t^{3}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-5410" title="F3 | Techniques for linear IVPs | ver. 5410"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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 {y'} = -3 \, {y} - \frac{10}{t} \hspace{2em} y( 1 )= -7" alt="t {y'} = -3 \, {y} - \frac{10}{t} \hspace{2em} y( 1 )= -7" title="t {y'} = -3 \, {y} - \frac{10}{t} \hspace{2em} y( 1 )= -7" data-latex="t {y'} = -3 \, {y} - \frac{10}{t} \hspace{2em} y( 1 )= -7"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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%7By'%7D%20=%20-3%20%5C,%20%7By%7D%20-%20%5Cfrac%7B10%7D%7Bt%7D%20%5Chspace%7B2em%7D%20y(%201%20)=%20-7" alt="t {y'} = -3 \, {y} - \frac{10}{t} \hspace{2em} y( 1 )= -7" title="t {y'} = -3 \, {y} - \frac{10}{t} \hspace{2em} y( 1 )= -7" data-latex="t {y'} = -3 \, {y} - \frac{10}{t} \hspace{2em} y( 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?{y} = -\frac{5}{t} - \frac{2}{t^{3}}" alt="{y} = -\frac{5}{t} - \frac{2}{t^{3}}" title="{y} = -\frac{5}{t} - \frac{2}{t^{3}}" data-latex="{y} = -\frac{5}{t} - \frac{2}{t^{3}}"/></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?%7By%7D%20=%20-%5Cfrac%7B5%7D%7Bt%7D%20-%20%5Cfrac%7B2%7D%7Bt%5E%7B3%7D%7D" alt="{y} = -\frac{5}{t} - \frac{2}{t^{3}}" title="{y} = -\frac{5}{t} - \frac{2}{t^{3}}" data-latex="{y} = -\frac{5}{t} - \frac{2}{t^{3}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-3893" title="F3 | Techniques for linear IVPs | ver. 3893"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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?8 \, t^{4} - 2 \, {y} = -{y'} t \hspace{2em} y( 1 )= -6" alt="8 \, t^{4} - 2 \, {y} = -{y'} t \hspace{2em} y( 1 )= -6" title="8 \, t^{4} - 2 \, {y} = -{y'} t \hspace{2em} y( 1 )= -6" data-latex="8 \, t^{4} - 2 \, {y} = -{y'} t \hspace{2em} y( 1 )= -6"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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?8%20%5C,%20t%5E%7B4%7D%20-%202%20%5C,%20%7By%7D%20=%20-%7By'%7D%20t%20%5Chspace%7B2em%7D%20y(%201%20)=%20-6" alt="8 \, t^{4} - 2 \, {y} = -{y'} t \hspace{2em} y( 1 )= -6" title="8 \, t^{4} - 2 \, {y} = -{y'} t \hspace{2em} y( 1 )= -6" data-latex="8 \, t^{4} - 2 \, {y} = -{y'} t \hspace{2em} y( 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?{y} = -4 \, t^{4} - 2 \, t^{2}" alt="{y} = -4 \, t^{4} - 2 \, t^{2}" title="{y} = -4 \, t^{4} - 2 \, t^{2}" data-latex="{y} = -4 \, t^{4} - 2 \, t^{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?%7By%7D%20=%20-4%20%5C,%20t%5E%7B4%7D%20-%202%20%5C,%20t%5E%7B2%7D" alt="{y} = -4 \, t^{4} - 2 \, t^{2}" title="{y} = -4 \, t^{4} - 2 \, t^{2}" data-latex="{y} = -4 \, t^{4} - 2 \, t^{2}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-9783" title="F3 | Techniques for linear IVPs | ver. 9783"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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?-15 \, t = -{y'} t + 4 \, {y} \hspace{2em} y( -1 )= 3" alt="-15 \, t = -{y'} t + 4 \, {y} \hspace{2em} y( -1 )= 3" title="-15 \, t = -{y'} t + 4 \, {y} \hspace{2em} y( -1 )= 3" data-latex="-15 \, t = -{y'} t + 4 \, {y} \hspace{2em} y( -1 )= 3"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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?-15%20%5C,%20t%20=%20-%7By'%7D%20t%20+%204%20%5C,%20%7By%7D%20%5Chspace%7B2em%7D%20y(%20-1%20)=%203" alt="-15 \, t = -{y'} t + 4 \, {y} \hspace{2em} y( -1 )= 3" title="-15 \, t = -{y'} t + 4 \, {y} \hspace{2em} y( -1 )= 3" data-latex="-15 \, t = -{y'} t + 4 \, {y} \hspace{2em} y( -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?{y} = -2 \, t^{4} - 5 \, t" alt="{y} = -2 \, t^{4} - 5 \, t" title="{y} = -2 \, t^{4} - 5 \, t" data-latex="{y} = -2 \, t^{4} - 5 \, t"/></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?%7By%7D%20=%20-2%20%5C,%20t%5E%7B4%7D%20-%205%20%5C,%20t" alt="{y} = -2 \, t^{4} - 5 \, t" title="{y} = -2 \, t^{4} - 5 \, t" data-latex="{y} = -2 \, t^{4} - 5 \, t"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-2215" title="F3 | Techniques for linear IVPs | ver. 2215"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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?3 \, {y} = 6 \, t^{3} - {y'} t \hspace{2em} y( -1 )= -2" alt="3 \, {y} = 6 \, t^{3} - {y'} t \hspace{2em} y( -1 )= -2" title="3 \, {y} = 6 \, t^{3} - {y'} t \hspace{2em} y( -1 )= -2" data-latex="3 \, {y} = 6 \, t^{3} - {y'} t \hspace{2em} y( -1 )= -2"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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?3%20%5C,%20%7By%7D%20=%206%20%5C,%20t%5E%7B3%7D%20-%20%7By'%7D%20t%20%5Chspace%7B2em%7D%20y(%20-1%20)=%20-2" alt="3 \, {y} = 6 \, t^{3} - {y'} t \hspace{2em} y( -1 )= -2" title="3 \, {y} = 6 \, t^{3} - {y'} t \hspace{2em} y( -1 )= -2" data-latex="3 \, {y} = 6 \, t^{3} - {y'} t \hspace{2em} y( -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?{y} = t^{3} + \frac{1}{t^{3}}" alt="{y} = t^{3} + \frac{1}{t^{3}}" title="{y} = t^{3} + \frac{1}{t^{3}}" data-latex="{y} = t^{3} + \frac{1}{t^{3}}"/></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?%7By%7D%20=%20t%5E%7B3%7D%20+%20%5Cfrac%7B1%7D%7Bt%5E%7B3%7D%7D" alt="{y} = t^{3} + \frac{1}{t^{3}}" title="{y} = t^{3} + \frac{1}{t^{3}}" data-latex="{y} = t^{3} + \frac{1}{t^{3}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-8652" title="F3 | Techniques for linear IVPs | ver. 8652"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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?4 \, {y} - \frac{25}{t} = {y'} t \hspace{2em} y( -1 )= -7" alt="4 \, {y} - \frac{25}{t} = {y'} t \hspace{2em} y( -1 )= -7" title="4 \, {y} - \frac{25}{t} = {y'} t \hspace{2em} y( -1 )= -7" data-latex="4 \, {y} - \frac{25}{t} = {y'} t \hspace{2em} y( -1 )= -7"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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?4%20%5C,%20%7By%7D%20-%20%5Cfrac%7B25%7D%7Bt%7D%20=%20%7By'%7D%20t%20%5Chspace%7B2em%7D%20y(%20-1%20)=%20-7" alt="4 \, {y} - \frac{25}{t} = {y'} t \hspace{2em} y( -1 )= -7" title="4 \, {y} - \frac{25}{t} = {y'} t \hspace{2em} y( -1 )= -7" data-latex="4 \, {y} - \frac{25}{t} = {y'} t \hspace{2em} y( -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?{y} = -2 \, t^{4} + \frac{5}{t}" alt="{y} = -2 \, t^{4} + \frac{5}{t}" title="{y} = -2 \, t^{4} + \frac{5}{t}" data-latex="{y} = -2 \, t^{4} + \frac{5}{t}"/></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?%7By%7D%20=%20-2%20%5C,%20t%5E%7B4%7D%20+%20%5Cfrac%7B5%7D%7Bt%7D" alt="{y} = -2 \, t^{4} + \frac{5}{t}" title="{y} = -2 \, t^{4} + \frac{5}{t}" data-latex="{y} = -2 \, t^{4} + \frac{5}{t}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-0825" title="F3 | Techniques for linear IVPs | ver. 0825"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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?5 \, {y} = -24 \, t^{3} - t {y'} \hspace{2em} y( 1 )= -4" alt="5 \, {y} = -24 \, t^{3} - t {y'} \hspace{2em} y( 1 )= -4" title="5 \, {y} = -24 \, t^{3} - t {y'} \hspace{2em} y( 1 )= -4" data-latex="5 \, {y} = -24 \, t^{3} - t {y'} \hspace{2em} y( 1 )= -4"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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?5%20%5C,%20%7By%7D%20=%20-24%20%5C,%20t%5E%7B3%7D%20-%20t%20%7By'%7D%20%5Chspace%7B2em%7D%20y(%201%20)=%20-4" alt="5 \, {y} = -24 \, t^{3} - t {y'} \hspace{2em} y( 1 )= -4" title="5 \, {y} = -24 \, t^{3} - t {y'} \hspace{2em} y( 1 )= -4" data-latex="5 \, {y} = -24 \, t^{3} - t {y'} \hspace{2em} y( 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?{y} = -3 \, t^{3} - \frac{1}{t^{5}}" alt="{y} = -3 \, t^{3} - \frac{1}{t^{5}}" title="{y} = -3 \, t^{3} - \frac{1}{t^{5}}" data-latex="{y} = -3 \, t^{3} - \frac{1}{t^{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?%7By%7D%20=%20-3%20%5C,%20t%5E%7B3%7D%20-%20%5Cfrac%7B1%7D%7Bt%5E%7B5%7D%7D" alt="{y} = -3 \, t^{3} - \frac{1}{t^{5}}" title="{y} = -3 \, t^{3} - \frac{1}{t^{5}}" data-latex="{y} = -3 \, t^{3} - \frac{1}{t^{5}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-3009" title="F3 | Techniques for linear IVPs | ver. 3009"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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 - 2 \, {y} + \frac{5}{t^{3}} = 0 \hspace{2em} y( -1 )= 1" alt="-{y'} t - 2 \, {y} + \frac{5}{t^{3}} = 0 \hspace{2em} y( -1 )= 1" title="-{y'} t - 2 \, {y} + \frac{5}{t^{3}} = 0 \hspace{2em} y( -1 )= 1" data-latex="-{y'} t - 2 \, {y} + \frac{5}{t^{3}} = 0 \hspace{2em} y( -1 )= 1"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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-%202%20%5C,%20%7By%7D%20+%20%5Cfrac%7B5%7D%7Bt%5E%7B3%7D%7D%20=%200%20%5Chspace%7B2em%7D%20y(%20-1%20)=%201" alt="-{y'} t - 2 \, {y} + \frac{5}{t^{3}} = 0 \hspace{2em} y( -1 )= 1" title="-{y'} t - 2 \, {y} + \frac{5}{t^{3}} = 0 \hspace{2em} y( -1 )= 1" data-latex="-{y'} t - 2 \, {y} + \frac{5}{t^{3}} = 0 \hspace{2em} y( -1 )= 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?{y} = -\frac{4}{t^{2}} - \frac{5}{t^{3}}" alt="{y} = -\frac{4}{t^{2}} - \frac{5}{t^{3}}" title="{y} = -\frac{4}{t^{2}} - \frac{5}{t^{3}}" data-latex="{y} = -\frac{4}{t^{2}} - \frac{5}{t^{3}}"/></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?%7By%7D%20=%20-%5Cfrac%7B4%7D%7Bt%5E%7B2%7D%7D%20-%20%5Cfrac%7B5%7D%7Bt%5E%7B3%7D%7D" alt="{y} = -\frac{4}{t^{2}} - \frac{5}{t^{3}}" title="{y} = -\frac{4}{t^{2}} - \frac{5}{t^{3}}" data-latex="{y} = -\frac{4}{t^{2}} - \frac{5}{t^{3}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-1011" title="F3 | Techniques for linear IVPs | ver. 1011"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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?3 \, {y} + \frac{18}{t^{3}} = t {y'} \hspace{2em} y( 1 )= -7" alt="3 \, {y} + \frac{18}{t^{3}} = t {y'} \hspace{2em} y( 1 )= -7" title="3 \, {y} + \frac{18}{t^{3}} = t {y'} \hspace{2em} y( 1 )= -7" data-latex="3 \, {y} + \frac{18}{t^{3}} = t {y'} \hspace{2em} y( 1 )= -7"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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?3%20%5C,%20%7By%7D%20+%20%5Cfrac%7B18%7D%7Bt%5E%7B3%7D%7D%20=%20t%20%7By'%7D%20%5Chspace%7B2em%7D%20y(%201%20)=%20-7" alt="3 \, {y} + \frac{18}{t^{3}} = t {y'} \hspace{2em} y( 1 )= -7" title="3 \, {y} + \frac{18}{t^{3}} = t {y'} \hspace{2em} y( 1 )= -7" data-latex="3 \, {y} + \frac{18}{t^{3}} = t {y'} \hspace{2em} y( 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?{y} = -4 \, t^{3} - \frac{3}{t^{3}}" alt="{y} = -4 \, t^{3} - \frac{3}{t^{3}}" title="{y} = -4 \, t^{3} - \frac{3}{t^{3}}" data-latex="{y} = -4 \, t^{3} - \frac{3}{t^{3}}"/></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?%7By%7D%20=%20-4%20%5C,%20t%5E%7B3%7D%20-%20%5Cfrac%7B3%7D%7Bt%5E%7B3%7D%7D" alt="{y} = -4 \, t^{3} - \frac{3}{t^{3}}" title="{y} = -4 \, t^{3} - \frac{3}{t^{3}}" data-latex="{y} = -4 \, t^{3} - \frac{3}{t^{3}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-9893" title="F3 | Techniques for linear IVPs | ver. 9893"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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 - \frac{20}{t} = 5 \, {y} \hspace{2em} y( 1 )= -3" alt="-{y'} t - \frac{20}{t} = 5 \, {y} \hspace{2em} y( 1 )= -3" title="-{y'} t - \frac{20}{t} = 5 \, {y} \hspace{2em} y( 1 )= -3" data-latex="-{y'} t - \frac{20}{t} = 5 \, {y} \hspace{2em} y( 1 )= -3"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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%5Cfrac%7B20%7D%7Bt%7D%20=%205%20%5C,%20%7By%7D%20%5Chspace%7B2em%7D%20y(%201%20)=%20-3" alt="-{y'} t - \frac{20}{t} = 5 \, {y} \hspace{2em} y( 1 )= -3" title="-{y'} t - \frac{20}{t} = 5 \, {y} \hspace{2em} y( 1 )= -3" data-latex="-{y'} t - \frac{20}{t} = 5 \, {y} \hspace{2em} y( 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?{y} = -\frac{5}{t} + \frac{2}{t^{5}}" alt="{y} = -\frac{5}{t} + \frac{2}{t^{5}}" title="{y} = -\frac{5}{t} + \frac{2}{t^{5}}" data-latex="{y} = -\frac{5}{t} + \frac{2}{t^{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?%7By%7D%20=%20-%5Cfrac%7B5%7D%7Bt%7D%20+%20%5Cfrac%7B2%7D%7Bt%5E%7B5%7D%7D" alt="{y} = -\frac{5}{t} + \frac{2}{t^{5}}" title="{y} = -\frac{5}{t} + \frac{2}{t^{5}}" data-latex="{y} = -\frac{5}{t} + \frac{2}{t^{5}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-5562" title="F3 | Techniques 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>F3.</strong></p><p>Find the solution to the given 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'} t - 5 \, {y} \hspace{2em} y( 1 )= 0" alt="-t^{4} = {y'} t - 5 \, {y} \hspace{2em} y( 1 )= 0" title="-t^{4} = {y'} t - 5 \, {y} \hspace{2em} y( 1 )= 0" data-latex="-t^{4} = {y'} t - 5 \, {y} \hspace{2em} y( 1 )= 0"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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%7B4%7D%20=%20%7By'%7D%20t%20-%205%20%5C,%20%7By%7D%20%5Chspace%7B2em%7D%20y(%201%20)=%200" alt="-t^{4} = {y'} t - 5 \, {y} \hspace{2em} y( 1 )= 0" title="-t^{4} = {y'} t - 5 \, {y} \hspace{2em} y( 1 )= 0" data-latex="-t^{4} = {y'} t - 5 \, {y} \hspace{2em} y( 1 )= 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?{y} = -t^{5} + t^{4}" alt="{y} = -t^{5} + t^{4}" title="{y} = -t^{5} + t^{4}" data-latex="{y} = -t^{5} + t^{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?%7By%7D%20=%20-t%5E%7B5%7D%20+%20t%5E%7B4%7D" alt="{y} = -t^{5} + t^{4}" title="{y} = -t^{5} + t^{4}" data-latex="{y} = -t^{5} + t^{4}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-3993" title="F3 | Techniques for linear IVPs | ver. 3993"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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 {y'} = 4 \, {y} + \frac{15}{t} \hspace{2em} y( 1 )= -2" alt="-t {y'} = 4 \, {y} + \frac{15}{t} \hspace{2em} y( 1 )= -2" title="-t {y'} = 4 \, {y} + \frac{15}{t} \hspace{2em} y( 1 )= -2" data-latex="-t {y'} = 4 \, {y} + \frac{15}{t} \hspace{2em} y( 1 )= -2"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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%7By'%7D%20=%204%20%5C,%20%7By%7D%20+%20%5Cfrac%7B15%7D%7Bt%7D%20%5Chspace%7B2em%7D%20y(%201%20)=%20-2" alt="-t {y'} = 4 \, {y} + \frac{15}{t} \hspace{2em} y( 1 )= -2" title="-t {y'} = 4 \, {y} + \frac{15}{t} \hspace{2em} y( 1 )= -2" data-latex="-t {y'} = 4 \, {y} + \frac{15}{t} \hspace{2em} y( 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?{y} = -\frac{5}{t} + \frac{3}{t^{4}}" alt="{y} = -\frac{5}{t} + \frac{3}{t^{4}}" title="{y} = -\frac{5}{t} + \frac{3}{t^{4}}" data-latex="{y} = -\frac{5}{t} + \frac{3}{t^{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?%7By%7D%20=%20-%5Cfrac%7B5%7D%7Bt%7D%20+%20%5Cfrac%7B3%7D%7Bt%5E%7B4%7D%7D" alt="{y} = -\frac{5}{t} + \frac{3}{t^{4}}" title="{y} = -\frac{5}{t} + \frac{3}{t^{4}}" data-latex="{y} = -\frac{5}{t} + \frac{3}{t^{4}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-3071" title="F3 | Techniques for linear IVPs | ver. 3071"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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?2 \, {y} - \frac{12}{t} = {y'} t \hspace{2em} y( 1 )= 2" alt="2 \, {y} - \frac{12}{t} = {y'} t \hspace{2em} y( 1 )= 2" title="2 \, {y} - \frac{12}{t} = {y'} t \hspace{2em} y( 1 )= 2" data-latex="2 \, {y} - \frac{12}{t} = {y'} t \hspace{2em} y( 1 )= 2"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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?2%20%5C,%20%7By%7D%20-%20%5Cfrac%7B12%7D%7Bt%7D%20=%20%7By'%7D%20t%20%5Chspace%7B2em%7D%20y(%201%20)=%202" alt="2 \, {y} - \frac{12}{t} = {y'} t \hspace{2em} y( 1 )= 2" title="2 \, {y} - \frac{12}{t} = {y'} t \hspace{2em} y( 1 )= 2" data-latex="2 \, {y} - \frac{12}{t} = {y'} t \hspace{2em} y( 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?{y} = -2 \, t^{2} + \frac{4}{t}" alt="{y} = -2 \, t^{2} + \frac{4}{t}" title="{y} = -2 \, t^{2} + \frac{4}{t}" data-latex="{y} = -2 \, t^{2} + \frac{4}{t}"/></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?%7By%7D%20=%20-2%20%5C,%20t%5E%7B2%7D%20+%20%5Cfrac%7B4%7D%7Bt%7D" alt="{y} = -2 \, t^{2} + \frac{4}{t}" title="{y} = -2 \, t^{2} + \frac{4}{t}" data-latex="{y} = -2 \, t^{2} + \frac{4}{t}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-7841" title="F3 | Techniques for linear IVPs | ver. 7841"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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 - \frac{5}{t^{3}} = -2 \, {y} \hspace{2em} y( 1 )= 4" alt="-{y'} t - \frac{5}{t^{3}} = -2 \, {y} \hspace{2em} y( 1 )= 4" title="-{y'} t - \frac{5}{t^{3}} = -2 \, {y} \hspace{2em} y( 1 )= 4" data-latex="-{y'} t - \frac{5}{t^{3}} = -2 \, {y} \hspace{2em} y( 1 )= 4"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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%5Cfrac%7B5%7D%7Bt%5E%7B3%7D%7D%20=%20-2%20%5C,%20%7By%7D%20%5Chspace%7B2em%7D%20y(%201%20)=%204" alt="-{y'} t - \frac{5}{t^{3}} = -2 \, {y} \hspace{2em} y( 1 )= 4" title="-{y'} t - \frac{5}{t^{3}} = -2 \, {y} \hspace{2em} y( 1 )= 4" data-latex="-{y'} t - \frac{5}{t^{3}} = -2 \, {y} \hspace{2em} y( 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?{y} = 3 \, t^{2} + \frac{1}{t^{3}}" alt="{y} = 3 \, t^{2} + \frac{1}{t^{3}}" title="{y} = 3 \, t^{2} + \frac{1}{t^{3}}" data-latex="{y} = 3 \, t^{2} + \frac{1}{t^{3}}"/></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?%7By%7D%20=%203%20%5C,%20t%5E%7B2%7D%20+%20%5Cfrac%7B1%7D%7Bt%5E%7B3%7D%7D" alt="{y} = 3 \, t^{2} + \frac{1}{t^{3}}" title="{y} = 3 \, t^{2} + \frac{1}{t^{3}}" data-latex="{y} = 3 \, t^{2} + \frac{1}{t^{3}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-2706" title="F3 | Techniques 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>F3.</strong></p><p>Find the solution to the given 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 = -4 \, {y} + \frac{30}{t^{2}} \hspace{2em} y( -1 )= 6" alt="-{y'} t = -4 \, {y} + \frac{30}{t^{2}} \hspace{2em} y( -1 )= 6" title="-{y'} t = -4 \, {y} + \frac{30}{t^{2}} \hspace{2em} y( -1 )= 6" data-latex="-{y'} t = -4 \, {y} + \frac{30}{t^{2}} \hspace{2em} y( -1 )= 6"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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=%20-4%20%5C,%20%7By%7D%20+%20%5Cfrac%7B30%7D%7Bt%5E%7B2%7D%7D%20%5Chspace%7B2em%7D%20y(%20-1%20)=%206" alt="-{y'} t = -4 \, {y} + \frac{30}{t^{2}} \hspace{2em} y( -1 )= 6" title="-{y'} t = -4 \, {y} + \frac{30}{t^{2}} \hspace{2em} y( -1 )= 6" data-latex="-{y'} t = -4 \, {y} + \frac{30}{t^{2}} \hspace{2em} y( -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?{y} = t^{4} + \frac{5}{t^{2}}" alt="{y} = t^{4} + \frac{5}{t^{2}}" title="{y} = t^{4} + \frac{5}{t^{2}}" data-latex="{y} = t^{4} + \frac{5}{t^{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?%7By%7D%20=%20t%5E%7B4%7D%20+%20%5Cfrac%7B5%7D%7Bt%5E%7B2%7D%7D" alt="{y} = t^{4} + \frac{5}{t^{2}}" title="{y} = t^{4} + \frac{5}{t^{2}}" data-latex="{y} = t^{4} + \frac{5}{t^{2}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-0639" title="F3 | Techniques for linear IVPs | ver. 0639"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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 + 5 \, {y} + \frac{20}{t} = 0 \hspace{2em} y( 1 )= -2" alt="{y'} t + 5 \, {y} + \frac{20}{t} = 0 \hspace{2em} y( 1 )= -2" title="{y'} t + 5 \, {y} + \frac{20}{t} = 0 \hspace{2em} y( 1 )= -2" data-latex="{y'} t + 5 \, {y} + \frac{20}{t} = 0 \hspace{2em} y( 1 )= -2"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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+%205%20%5C,%20%7By%7D%20+%20%5Cfrac%7B20%7D%7Bt%7D%20=%200%20%5Chspace%7B2em%7D%20y(%201%20)=%20-2" alt="{y'} t + 5 \, {y} + \frac{20}{t} = 0 \hspace{2em} y( 1 )= -2" title="{y'} t + 5 \, {y} + \frac{20}{t} = 0 \hspace{2em} y( 1 )= -2" data-latex="{y'} t + 5 \, {y} + \frac{20}{t} = 0 \hspace{2em} y( 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?{y} = -\frac{5}{t} + \frac{3}{t^{5}}" alt="{y} = -\frac{5}{t} + \frac{3}{t^{5}}" title="{y} = -\frac{5}{t} + \frac{3}{t^{5}}" data-latex="{y} = -\frac{5}{t} + \frac{3}{t^{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?%7By%7D%20=%20-%5Cfrac%7B5%7D%7Bt%7D%20+%20%5Cfrac%7B3%7D%7Bt%5E%7B5%7D%7D" alt="{y} = -\frac{5}{t} + \frac{3}{t^{5}}" title="{y} = -\frac{5}{t} + \frac{3}{t^{5}}" data-latex="{y} = -\frac{5}{t} + \frac{3}{t^{5}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-5660" title="F3 | Techniques for linear IVPs | ver. 5660"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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?-5 \, t^{3} = -{y'} t - 2 \, {y} \hspace{2em} y( 1 )= -2" alt="-5 \, t^{3} = -{y'} t - 2 \, {y} \hspace{2em} y( 1 )= -2" title="-5 \, t^{3} = -{y'} t - 2 \, {y} \hspace{2em} y( 1 )= -2" data-latex="-5 \, t^{3} = -{y'} t - 2 \, {y} \hspace{2em} y( 1 )= -2"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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?-5%20%5C,%20t%5E%7B3%7D%20=%20-%7By'%7D%20t%20-%202%20%5C,%20%7By%7D%20%5Chspace%7B2em%7D%20y(%201%20)=%20-2" alt="-5 \, t^{3} = -{y'} t - 2 \, {y} \hspace{2em} y( 1 )= -2" title="-5 \, t^{3} = -{y'} t - 2 \, {y} \hspace{2em} y( 1 )= -2" data-latex="-5 \, t^{3} = -{y'} t - 2 \, {y} \hspace{2em} y( 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?{y} = t^{3} - \frac{3}{t^{2}}" alt="{y} = t^{3} - \frac{3}{t^{2}}" title="{y} = t^{3} - \frac{3}{t^{2}}" data-latex="{y} = t^{3} - \frac{3}{t^{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?%7By%7D%20=%20t%5E%7B3%7D%20-%20%5Cfrac%7B3%7D%7Bt%5E%7B2%7D%7D" alt="{y} = t^{3} - \frac{3}{t^{2}}" title="{y} = t^{3} - \frac{3}{t^{2}}" data-latex="{y} = t^{3} - \frac{3}{t^{2}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-5691" title="F3 | Techniques for linear IVPs | ver. 5691"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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 + 4 \, {y} = -28 \, t^{3} \hspace{2em} y( -1 )= 0" alt="{y'} t + 4 \, {y} = -28 \, t^{3} \hspace{2em} y( -1 )= 0" title="{y'} t + 4 \, {y} = -28 \, t^{3} \hspace{2em} y( -1 )= 0" data-latex="{y'} t + 4 \, {y} = -28 \, t^{3} \hspace{2em} y( -1 )= 0"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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+%204%20%5C,%20%7By%7D%20=%20-28%20%5C,%20t%5E%7B3%7D%20%5Chspace%7B2em%7D%20y(%20-1%20)=%200" alt="{y'} t + 4 \, {y} = -28 \, t^{3} \hspace{2em} y( -1 )= 0" title="{y'} t + 4 \, {y} = -28 \, t^{3} \hspace{2em} y( -1 )= 0" data-latex="{y'} t + 4 \, {y} = -28 \, t^{3} \hspace{2em} y( -1 )= 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?{y} = -4 \, t^{3} - \frac{4}{t^{4}}" alt="{y} = -4 \, t^{3} - \frac{4}{t^{4}}" title="{y} = -4 \, t^{3} - \frac{4}{t^{4}}" data-latex="{y} = -4 \, t^{3} - \frac{4}{t^{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?%7By%7D%20=%20-4%20%5C,%20t%5E%7B3%7D%20-%20%5Cfrac%7B4%7D%7Bt%5E%7B4%7D%7D" alt="{y} = -4 \, t^{3} - \frac{4}{t^{4}}" title="{y} = -4 \, t^{3} - \frac{4}{t^{4}}" data-latex="{y} = -4 \, t^{3} - \frac{4}{t^{4}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-5580" title="F3 | Techniques for linear IVPs | ver. 5580"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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?2 \, {y} = t {y'} + t \hspace{2em} y( 1 )= 5" alt="2 \, {y} = t {y'} + t \hspace{2em} y( 1 )= 5" title="2 \, {y} = t {y'} + t \hspace{2em} y( 1 )= 5" data-latex="2 \, {y} = t {y'} + t \hspace{2em} y( 1 )= 5"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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?2%20%5C,%20%7By%7D%20=%20t%20%7By'%7D%20+%20t%20%5Chspace%7B2em%7D%20y(%201%20)=%205" alt="2 \, {y} = t {y'} + t \hspace{2em} y( 1 )= 5" title="2 \, {y} = t {y'} + t \hspace{2em} y( 1 )= 5" data-latex="2 \, {y} = t {y'} + t \hspace{2em} y( 1 )= 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?{y} = 4 \, t^{2} + t" alt="{y} = 4 \, t^{2} + t" title="{y} = 4 \, t^{2} + t" data-latex="{y} = 4 \, t^{2} + t"/></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?%7By%7D%20=%204%20%5C,%20t%5E%7B2%7D%20+%20t" alt="{y} = 4 \, t^{2} + t" title="{y} = 4 \, t^{2} + t" data-latex="{y} = 4 \, t^{2} + t"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-1665" title="F3 | Techniques for linear IVPs | ver. 1665"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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?-2 \, {y} + 3 \, t = {y'} t \hspace{2em} y( 1 )= 4" alt="-2 \, {y} + 3 \, t = {y'} t \hspace{2em} y( 1 )= 4" title="-2 \, {y} + 3 \, t = {y'} t \hspace{2em} y( 1 )= 4" data-latex="-2 \, {y} + 3 \, t = {y'} t \hspace{2em} y( 1 )= 4"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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?-2%20%5C,%20%7By%7D%20+%203%20%5C,%20t%20=%20%7By'%7D%20t%20%5Chspace%7B2em%7D%20y(%201%20)=%204" alt="-2 \, {y} + 3 \, t = {y'} t \hspace{2em} y( 1 )= 4" title="-2 \, {y} + 3 \, t = {y'} t \hspace{2em} y( 1 )= 4" data-latex="-2 \, {y} + 3 \, t = {y'} t \hspace{2em} y( 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?{y} = t + \frac{3}{t^{2}}" alt="{y} = t + \frac{3}{t^{2}}" title="{y} = t + \frac{3}{t^{2}}" data-latex="{y} = t + \frac{3}{t^{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?%7By%7D%20=%20t%20+%20%5Cfrac%7B3%7D%7Bt%5E%7B2%7D%7D" alt="{y} = t + \frac{3}{t^{2}}" title="{y} = t + \frac{3}{t^{2}}" data-latex="{y} = t + \frac{3}{t^{2}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-9844" title="F3 | Techniques for linear IVPs | ver. 9844"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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 {y'} + 5 \, {y} = 4 \, t \hspace{2em} y( 1 )= -2" alt="-t {y'} + 5 \, {y} = 4 \, t \hspace{2em} y( 1 )= -2" title="-t {y'} + 5 \, {y} = 4 \, t \hspace{2em} y( 1 )= -2" data-latex="-t {y'} + 5 \, {y} = 4 \, t \hspace{2em} y( 1 )= -2"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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%7By'%7D%20+%205%20%5C,%20%7By%7D%20=%204%20%5C,%20t%20%5Chspace%7B2em%7D%20y(%201%20)=%20-2" alt="-t {y'} + 5 \, {y} = 4 \, t \hspace{2em} y( 1 )= -2" title="-t {y'} + 5 \, {y} = 4 \, t \hspace{2em} y( 1 )= -2" data-latex="-t {y'} + 5 \, {y} = 4 \, t \hspace{2em} y( 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?{y} = -3 \, t^{5} + t" alt="{y} = -3 \, t^{5} + t" title="{y} = -3 \, t^{5} + t" data-latex="{y} = -3 \, t^{5} + t"/></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?%7By%7D%20=%20-3%20%5C,%20t%5E%7B5%7D%20+%20t" alt="{y} = -3 \, t^{5} + t" title="{y} = -3 \, t^{5} + t" data-latex="{y} = -3 \, t^{5} + t"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-2984" title="F3 | Techniques for linear IVPs | ver. 2984"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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?-25 \, t^{3} = -{y'} t - 2 \, {y} \hspace{2em} y( 1 )= 9" alt="-25 \, t^{3} = -{y'} t - 2 \, {y} \hspace{2em} y( 1 )= 9" title="-25 \, t^{3} = -{y'} t - 2 \, {y} \hspace{2em} y( 1 )= 9" data-latex="-25 \, t^{3} = -{y'} t - 2 \, {y} \hspace{2em} y( 1 )= 9"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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?-25%20%5C,%20t%5E%7B3%7D%20=%20-%7By'%7D%20t%20-%202%20%5C,%20%7By%7D%20%5Chspace%7B2em%7D%20y(%201%20)=%209" alt="-25 \, t^{3} = -{y'} t - 2 \, {y} \hspace{2em} y( 1 )= 9" title="-25 \, t^{3} = -{y'} t - 2 \, {y} \hspace{2em} y( 1 )= 9" data-latex="-25 \, t^{3} = -{y'} t - 2 \, {y} \hspace{2em} y( 1 )= 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?{y} = 5 \, t^{3} + \frac{4}{t^{2}}" alt="{y} = 5 \, t^{3} + \frac{4}{t^{2}}" title="{y} = 5 \, t^{3} + \frac{4}{t^{2}}" data-latex="{y} = 5 \, t^{3} + \frac{4}{t^{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?%7By%7D%20=%205%20%5C,%20t%5E%7B3%7D%20+%20%5Cfrac%7B4%7D%7Bt%5E%7B2%7D%7D" alt="{y} = 5 \, t^{3} + \frac{4}{t^{2}}" title="{y} = 5 \, t^{3} + \frac{4}{t^{2}}" data-latex="{y} = 5 \, t^{3} + \frac{4}{t^{2}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-3569" title="F3 | Techniques for linear IVPs | ver. 3569"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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?3 \, {y} - \frac{6}{t^{3}} = t {y'} \hspace{2em} y( -1 )= 0" alt="3 \, {y} - \frac{6}{t^{3}} = t {y'} \hspace{2em} y( -1 )= 0" title="3 \, {y} - \frac{6}{t^{3}} = t {y'} \hspace{2em} y( -1 )= 0" data-latex="3 \, {y} - \frac{6}{t^{3}} = t {y'} \hspace{2em} y( -1 )= 0"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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?3%20%5C,%20%7By%7D%20-%20%5Cfrac%7B6%7D%7Bt%5E%7B3%7D%7D%20=%20t%20%7By'%7D%20%5Chspace%7B2em%7D%20y(%20-1%20)=%200" alt="3 \, {y} - \frac{6}{t^{3}} = t {y'} \hspace{2em} y( -1 )= 0" title="3 \, {y} - \frac{6}{t^{3}} = t {y'} \hspace{2em} y( -1 )= 0" data-latex="3 \, {y} - \frac{6}{t^{3}} = t {y'} \hspace{2em} y( -1 )= 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?{y} = -t^{3} + \frac{1}{t^{3}}" alt="{y} = -t^{3} + \frac{1}{t^{3}}" title="{y} = -t^{3} + \frac{1}{t^{3}}" data-latex="{y} = -t^{3} + \frac{1}{t^{3}}"/></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?%7By%7D%20=%20-t%5E%7B3%7D%20+%20%5Cfrac%7B1%7D%7Bt%5E%7B3%7D%7D" alt="{y} = -t^{3} + \frac{1}{t^{3}}" title="{y} = -t^{3} + \frac{1}{t^{3}}" data-latex="{y} = -t^{3} + \frac{1}{t^{3}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-2758" title="F3 | Techniques for linear IVPs | ver. 2758"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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?3 \, {y} + \frac{1}{t^{2}} = -t {y'} \hspace{2em} y( -1 )= -2" alt="3 \, {y} + \frac{1}{t^{2}} = -t {y'} \hspace{2em} y( -1 )= -2" title="3 \, {y} + \frac{1}{t^{2}} = -t {y'} \hspace{2em} y( -1 )= -2" data-latex="3 \, {y} + \frac{1}{t^{2}} = -t {y'} \hspace{2em} y( -1 )= -2"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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?3%20%5C,%20%7By%7D%20+%20%5Cfrac%7B1%7D%7Bt%5E%7B2%7D%7D%20=%20-t%20%7By'%7D%20%5Chspace%7B2em%7D%20y(%20-1%20)=%20-2" alt="3 \, {y} + \frac{1}{t^{2}} = -t {y'} \hspace{2em} y( -1 )= -2" title="3 \, {y} + \frac{1}{t^{2}} = -t {y'} \hspace{2em} y( -1 )= -2" data-latex="3 \, {y} + \frac{1}{t^{2}} = -t {y'} \hspace{2em} y( -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?{y} = -\frac{1}{t^{2}} + \frac{1}{t^{3}}" alt="{y} = -\frac{1}{t^{2}} + \frac{1}{t^{3}}" title="{y} = -\frac{1}{t^{2}} + \frac{1}{t^{3}}" data-latex="{y} = -\frac{1}{t^{2}} + \frac{1}{t^{3}}"/></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?%7By%7D%20=%20-%5Cfrac%7B1%7D%7Bt%5E%7B2%7D%7D%20+%20%5Cfrac%7B1%7D%7Bt%5E%7B3%7D%7D" alt="{y} = -\frac{1}{t^{2}} + \frac{1}{t^{3}}" title="{y} = -\frac{1}{t^{2}} + \frac{1}{t^{3}}" data-latex="{y} = -\frac{1}{t^{2}} + \frac{1}{t^{3}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-4599" title="F3 | Techniques for linear IVPs | ver. 4599"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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 + \frac{5}{t^{4}} = -5 \, {y} \hspace{2em} y( 1 )= -1" alt="{y'} t + \frac{5}{t^{4}} = -5 \, {y} \hspace{2em} y( 1 )= -1" title="{y'} t + \frac{5}{t^{4}} = -5 \, {y} \hspace{2em} y( 1 )= -1" data-latex="{y'} t + \frac{5}{t^{4}} = -5 \, {y} \hspace{2em} y( 1 )= -1"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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%5Cfrac%7B5%7D%7Bt%5E%7B4%7D%7D%20=%20-5%20%5C,%20%7By%7D%20%5Chspace%7B2em%7D%20y(%201%20)=%20-1" alt="{y'} t + \frac{5}{t^{4}} = -5 \, {y} \hspace{2em} y( 1 )= -1" title="{y'} t + \frac{5}{t^{4}} = -5 \, {y} \hspace{2em} y( 1 )= -1" data-latex="{y'} t + \frac{5}{t^{4}} = -5 \, {y} \hspace{2em} y( 1 )= -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?{y} = -\frac{5}{t^{4}} + \frac{4}{t^{5}}" alt="{y} = -\frac{5}{t^{4}} + \frac{4}{t^{5}}" title="{y} = -\frac{5}{t^{4}} + \frac{4}{t^{5}}" data-latex="{y} = -\frac{5}{t^{4}} + \frac{4}{t^{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?%7By%7D%20=%20-%5Cfrac%7B5%7D%7Bt%5E%7B4%7D%7D%20+%20%5Cfrac%7B4%7D%7Bt%5E%7B5%7D%7D" alt="{y} = -\frac{5}{t^{4}} + \frac{4}{t^{5}}" title="{y} = -\frac{5}{t^{4}} + \frac{4}{t^{5}}" data-latex="{y} = -\frac{5}{t^{4}} + \frac{4}{t^{5}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-4034" title="F3 | Techniques for linear IVPs | ver. 4034"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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 = -t {y'} - 15 \, t + 4 \, {y} \hspace{2em} y( 1 )= 9" alt="0 = -t {y'} - 15 \, t + 4 \, {y} \hspace{2em} y( 1 )= 9" title="0 = -t {y'} - 15 \, t + 4 \, {y} \hspace{2em} y( 1 )= 9" data-latex="0 = -t {y'} - 15 \, t + 4 \, {y} \hspace{2em} y( 1 )= 9"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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-t%20%7By'%7D%20-%2015%20%5C,%20t%20+%204%20%5C,%20%7By%7D%20%5Chspace%7B2em%7D%20y(%201%20)=%209" alt="0 = -t {y'} - 15 \, t + 4 \, {y} \hspace{2em} y( 1 )= 9" title="0 = -t {y'} - 15 \, t + 4 \, {y} \hspace{2em} y( 1 )= 9" data-latex="0 = -t {y'} - 15 \, t + 4 \, {y} \hspace{2em} y( 1 )= 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?{y} = 4 \, t^{4} + 5 \, t" alt="{y} = 4 \, t^{4} + 5 \, t" title="{y} = 4 \, t^{4} + 5 \, t" data-latex="{y} = 4 \, t^{4} + 5 \, t"/></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?%7By%7D%20=%204%20%5C,%20t%5E%7B4%7D%20+%205%20%5C,%20t" alt="{y} = 4 \, t^{4} + 5 \, t" title="{y} = 4 \, t^{4} + 5 \, t" data-latex="{y} = 4 \, t^{4} + 5 \, t"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-2048" title="F3 | Techniques for linear IVPs | ver. 2048"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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'} t - 25 \, t^{2} - 3 \, {y} \hspace{2em} y( -1 )= -8" alt="0 = -{y'} t - 25 \, t^{2} - 3 \, {y} \hspace{2em} y( -1 )= -8" title="0 = -{y'} t - 25 \, t^{2} - 3 \, {y} \hspace{2em} y( -1 )= -8" data-latex="0 = -{y'} t - 25 \, t^{2} - 3 \, {y} \hspace{2em} y( -1 )= -8"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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%20t%20-%2025%20%5C,%20t%5E%7B2%7D%20-%203%20%5C,%20%7By%7D%20%5Chspace%7B2em%7D%20y(%20-1%20)=%20-8" alt="0 = -{y'} t - 25 \, t^{2} - 3 \, {y} \hspace{2em} y( -1 )= -8" title="0 = -{y'} t - 25 \, t^{2} - 3 \, {y} \hspace{2em} y( -1 )= -8" data-latex="0 = -{y'} t - 25 \, t^{2} - 3 \, {y} \hspace{2em} y( -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?{y} = -5 \, t^{2} + \frac{3}{t^{3}}" alt="{y} = -5 \, t^{2} + \frac{3}{t^{3}}" title="{y} = -5 \, t^{2} + \frac{3}{t^{3}}" data-latex="{y} = -5 \, t^{2} + \frac{3}{t^{3}}"/></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?%7By%7D%20=%20-5%20%5C,%20t%5E%7B2%7D%20+%20%5Cfrac%7B3%7D%7Bt%5E%7B3%7D%7D" alt="{y} = -5 \, t^{2} + \frac{3}{t^{3}}" title="{y} = -5 \, t^{2} + \frac{3}{t^{3}}" data-latex="{y} = -5 \, t^{2} + \frac{3}{t^{3}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-1451" title="F3 | Techniques for linear IVPs | ver. 1451"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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?2 \, t^{4} = t {y'} - 2 \, {y} \hspace{2em} y( -1 )= -3" alt="2 \, t^{4} = t {y'} - 2 \, {y} \hspace{2em} y( -1 )= -3" title="2 \, t^{4} = t {y'} - 2 \, {y} \hspace{2em} y( -1 )= -3" data-latex="2 \, t^{4} = t {y'} - 2 \, {y} \hspace{2em} y( -1 )= -3"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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?2%20%5C,%20t%5E%7B4%7D%20=%20t%20%7By'%7D%20-%202%20%5C,%20%7By%7D%20%5Chspace%7B2em%7D%20y(%20-1%20)=%20-3" alt="2 \, t^{4} = t {y'} - 2 \, {y} \hspace{2em} y( -1 )= -3" title="2 \, t^{4} = t {y'} - 2 \, {y} \hspace{2em} y( -1 )= -3" data-latex="2 \, t^{4} = t {y'} - 2 \, {y} \hspace{2em} y( -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?{y} = t^{4} - 4 \, t^{2}" alt="{y} = t^{4} - 4 \, t^{2}" title="{y} = t^{4} - 4 \, t^{2}" data-latex="{y} = t^{4} - 4 \, t^{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?%7By%7D%20=%20t%5E%7B4%7D%20-%204%20%5C,%20t%5E%7B2%7D" alt="{y} = t^{4} - 4 \, t^{2}" title="{y} = t^{4} - 4 \, t^{2}" data-latex="{y} = t^{4} - 4 \, t^{2}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-6440" title="F3 | Techniques for linear IVPs | ver. 6440"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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'} t + 3 \, {y} - 6 \, t \hspace{2em} y( 1 )= 2" alt="0 = -{y'} t + 3 \, {y} - 6 \, t \hspace{2em} y( 1 )= 2" title="0 = -{y'} t + 3 \, {y} - 6 \, t \hspace{2em} y( 1 )= 2" data-latex="0 = -{y'} t + 3 \, {y} - 6 \, t \hspace{2em} y( 1 )= 2"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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%20t%20+%203%20%5C,%20%7By%7D%20-%206%20%5C,%20t%20%5Chspace%7B2em%7D%20y(%201%20)=%202" alt="0 = -{y'} t + 3 \, {y} - 6 \, t \hspace{2em} y( 1 )= 2" title="0 = -{y'} t + 3 \, {y} - 6 \, t \hspace{2em} y( 1 )= 2" data-latex="0 = -{y'} t + 3 \, {y} - 6 \, t \hspace{2em} y( 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?{y} = -t^{3} + 3 \, t" alt="{y} = -t^{3} + 3 \, t" title="{y} = -t^{3} + 3 \, t" data-latex="{y} = -t^{3} + 3 \, t"/></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?%7By%7D%20=%20-t%5E%7B3%7D%20+%203%20%5C,%20t" alt="{y} = -t^{3} + 3 \, t" title="{y} = -t^{3} + 3 \, t" data-latex="{y} = -t^{3} + 3 \, t"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-7749" title="F3 | Techniques for linear IVPs | ver. 7749"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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?-4 \, t^{2} - t {y'} + 4 \, {y} = 0 \hspace{2em} y( -1 )= 3" alt="-4 \, t^{2} - t {y'} + 4 \, {y} = 0 \hspace{2em} y( -1 )= 3" title="-4 \, t^{2} - t {y'} + 4 \, {y} = 0 \hspace{2em} y( -1 )= 3" data-latex="-4 \, t^{2} - t {y'} + 4 \, {y} = 0 \hspace{2em} y( -1 )= 3"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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?-4%20%5C,%20t%5E%7B2%7D%20-%20t%20%7By'%7D%20+%204%20%5C,%20%7By%7D%20=%200%20%5Chspace%7B2em%7D%20y(%20-1%20)=%203" alt="-4 \, t^{2} - t {y'} + 4 \, {y} = 0 \hspace{2em} y( -1 )= 3" title="-4 \, t^{2} - t {y'} + 4 \, {y} = 0 \hspace{2em} y( -1 )= 3" data-latex="-4 \, t^{2} - t {y'} + 4 \, {y} = 0 \hspace{2em} y( -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?{y} = t^{4} + 2 \, t^{2}" alt="{y} = t^{4} + 2 \, t^{2}" title="{y} = t^{4} + 2 \, t^{2}" data-latex="{y} = t^{4} + 2 \, t^{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?%7By%7D%20=%20t%5E%7B4%7D%20+%202%20%5C,%20t%5E%7B2%7D" alt="{y} = t^{4} + 2 \, t^{2}" title="{y} = t^{4} + 2 \, t^{2}" data-latex="{y} = t^{4} + 2 \, t^{2}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-2768" title="F3 | Techniques for linear IVPs | ver. 2768"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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'} t + 5 \, t^{2} + 3 \, {y} \hspace{2em} y( 1 )= 0" alt="0 = {y'} t + 5 \, t^{2} + 3 \, {y} \hspace{2em} y( 1 )= 0" title="0 = {y'} t + 5 \, t^{2} + 3 \, {y} \hspace{2em} y( 1 )= 0" data-latex="0 = {y'} t + 5 \, t^{2} + 3 \, {y} \hspace{2em} y( 1 )= 0"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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%20t%20+%205%20%5C,%20t%5E%7B2%7D%20+%203%20%5C,%20%7By%7D%20%5Chspace%7B2em%7D%20y(%201%20)=%200" alt="0 = {y'} t + 5 \, t^{2} + 3 \, {y} \hspace{2em} y( 1 )= 0" title="0 = {y'} t + 5 \, t^{2} + 3 \, {y} \hspace{2em} y( 1 )= 0" data-latex="0 = {y'} t + 5 \, t^{2} + 3 \, {y} \hspace{2em} y( 1 )= 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?{y} = -t^{2} + \frac{1}{t^{3}}" alt="{y} = -t^{2} + \frac{1}{t^{3}}" title="{y} = -t^{2} + \frac{1}{t^{3}}" data-latex="{y} = -t^{2} + \frac{1}{t^{3}}"/></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?%7By%7D%20=%20-t%5E%7B2%7D%20+%20%5Cfrac%7B1%7D%7Bt%5E%7B3%7D%7D" alt="{y} = -t^{2} + \frac{1}{t^{3}}" title="{y} = -t^{2} + \frac{1}{t^{3}}" data-latex="{y} = -t^{2} + \frac{1}{t^{3}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-0592" title="F3 | Techniques for linear IVPs | ver. 0592"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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 {y'} - 5 \, {y} = \frac{8}{t^{3}} \hspace{2em} y( 1 )= 0" alt="t {y'} - 5 \, {y} = \frac{8}{t^{3}} \hspace{2em} y( 1 )= 0" title="t {y'} - 5 \, {y} = \frac{8}{t^{3}} \hspace{2em} y( 1 )= 0" data-latex="t {y'} - 5 \, {y} = \frac{8}{t^{3}} \hspace{2em} y( 1 )= 0"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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%7By'%7D%20-%205%20%5C,%20%7By%7D%20=%20%5Cfrac%7B8%7D%7Bt%5E%7B3%7D%7D%20%5Chspace%7B2em%7D%20y(%201%20)=%200" alt="t {y'} - 5 \, {y} = \frac{8}{t^{3}} \hspace{2em} y( 1 )= 0" title="t {y'} - 5 \, {y} = \frac{8}{t^{3}} \hspace{2em} y( 1 )= 0" data-latex="t {y'} - 5 \, {y} = \frac{8}{t^{3}} \hspace{2em} y( 1 )= 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?{y} = t^{5} - \frac{1}{t^{3}}" alt="{y} = t^{5} - \frac{1}{t^{3}}" title="{y} = t^{5} - \frac{1}{t^{3}}" data-latex="{y} = t^{5} - \frac{1}{t^{3}}"/></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?%7By%7D%20=%20t%5E%7B5%7D%20-%20%5Cfrac%7B1%7D%7Bt%5E%7B3%7D%7D" alt="{y} = t^{5} - \frac{1}{t^{3}}" title="{y} = t^{5} - \frac{1}{t^{3}}" data-latex="{y} = t^{5} - \frac{1}{t^{3}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-1635" title="F3 | Techniques for linear IVPs | ver. 1635"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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 = 5 \, t^{3} - {y'} t + 4 \, {y} \hspace{2em} y( -1 )= 3" alt="0 = 5 \, t^{3} - {y'} t + 4 \, {y} \hspace{2em} y( -1 )= 3" title="0 = 5 \, t^{3} - {y'} t + 4 \, {y} \hspace{2em} y( -1 )= 3" data-latex="0 = 5 \, t^{3} - {y'} t + 4 \, {y} \hspace{2em} y( -1 )= 3"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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=%205%20%5C,%20t%5E%7B3%7D%20-%20%7By'%7D%20t%20+%204%20%5C,%20%7By%7D%20%5Chspace%7B2em%7D%20y(%20-1%20)=%203" alt="0 = 5 \, t^{3} - {y'} t + 4 \, {y} \hspace{2em} y( -1 )= 3" title="0 = 5 \, t^{3} - {y'} t + 4 \, {y} \hspace{2em} y( -1 )= 3" data-latex="0 = 5 \, t^{3} - {y'} t + 4 \, {y} \hspace{2em} y( -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?{y} = -2 \, t^{4} - 5 \, t^{3}" alt="{y} = -2 \, t^{4} - 5 \, t^{3}" title="{y} = -2 \, t^{4} - 5 \, t^{3}" data-latex="{y} = -2 \, t^{4} - 5 \, t^{3}"/></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?%7By%7D%20=%20-2%20%5C,%20t%5E%7B4%7D%20-%205%20%5C,%20t%5E%7B3%7D" alt="{y} = -2 \, t^{4} - 5 \, t^{3}" title="{y} = -2 \, t^{4} - 5 \, t^{3}" data-latex="{y} = -2 \, t^{4} - 5 \, t^{3}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-4797" title="F3 | Techniques for linear IVPs | ver. 4797"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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?-4 \, {y} = {y'} t + 6 \, t^{2} \hspace{2em} y( -1 )= 0" alt="-4 \, {y} = {y'} t + 6 \, t^{2} \hspace{2em} y( -1 )= 0" title="-4 \, {y} = {y'} t + 6 \, t^{2} \hspace{2em} y( -1 )= 0" data-latex="-4 \, {y} = {y'} t + 6 \, t^{2} \hspace{2em} y( -1 )= 0"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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?-4%20%5C,%20%7By%7D%20=%20%7By'%7D%20t%20+%206%20%5C,%20t%5E%7B2%7D%20%5Chspace%7B2em%7D%20y(%20-1%20)=%200" alt="-4 \, {y} = {y'} t + 6 \, t^{2} \hspace{2em} y( -1 )= 0" title="-4 \, {y} = {y'} t + 6 \, t^{2} \hspace{2em} y( -1 )= 0" data-latex="-4 \, {y} = {y'} t + 6 \, t^{2} \hspace{2em} y( -1 )= 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?{y} = -t^{2} + \frac{1}{t^{4}}" alt="{y} = -t^{2} + \frac{1}{t^{4}}" title="{y} = -t^{2} + \frac{1}{t^{4}}" data-latex="{y} = -t^{2} + \frac{1}{t^{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?%7By%7D%20=%20-t%5E%7B2%7D%20+%20%5Cfrac%7B1%7D%7Bt%5E%7B4%7D%7D" alt="{y} = -t^{2} + \frac{1}{t^{4}}" title="{y} = -t^{2} + \frac{1}{t^{4}}" data-latex="{y} = -t^{2} + \frac{1}{t^{4}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-2256" title="F3 | Techniques for linear IVPs | ver. 2256"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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?-5 \, {y} + 16 \, t = -{y'} t \hspace{2em} y( 1 )= 8" alt="-5 \, {y} + 16 \, t = -{y'} t \hspace{2em} y( 1 )= 8" title="-5 \, {y} + 16 \, t = -{y'} t \hspace{2em} y( 1 )= 8" data-latex="-5 \, {y} + 16 \, t = -{y'} t \hspace{2em} y( 1 )= 8"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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?-5%20%5C,%20%7By%7D%20+%2016%20%5C,%20t%20=%20-%7By'%7D%20t%20%5Chspace%7B2em%7D%20y(%201%20)=%208" alt="-5 \, {y} + 16 \, t = -{y'} t \hspace{2em} y( 1 )= 8" title="-5 \, {y} + 16 \, t = -{y'} t \hspace{2em} y( 1 )= 8" data-latex="-5 \, {y} + 16 \, t = -{y'} t \hspace{2em} y( 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?{y} = 4 \, t^{5} + 4 \, t" alt="{y} = 4 \, t^{5} + 4 \, t" title="{y} = 4 \, t^{5} + 4 \, t" data-latex="{y} = 4 \, t^{5} + 4 \, t"/></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?%7By%7D%20=%204%20%5C,%20t%5E%7B5%7D%20+%204%20%5C,%20t" alt="{y} = 4 \, t^{5} + 4 \, t" title="{y} = 4 \, t^{5} + 4 \, t" data-latex="{y} = 4 \, t^{5} + 4 \, t"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-8797" title="F3 | Techniques for linear IVPs | ver. 8797"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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?4 \, {y} = -{y'} t - 5 \, t \hspace{2em} y( 1 )= 3" alt="4 \, {y} = -{y'} t - 5 \, t \hspace{2em} y( 1 )= 3" title="4 \, {y} = -{y'} t - 5 \, t \hspace{2em} y( 1 )= 3" data-latex="4 \, {y} = -{y'} t - 5 \, t \hspace{2em} y( 1 )= 3"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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?4%20%5C,%20%7By%7D%20=%20-%7By'%7D%20t%20-%205%20%5C,%20t%20%5Chspace%7B2em%7D%20y(%201%20)=%203" alt="4 \, {y} = -{y'} t - 5 \, t \hspace{2em} y( 1 )= 3" title="4 \, {y} = -{y'} t - 5 \, t \hspace{2em} y( 1 )= 3" data-latex="4 \, {y} = -{y'} t - 5 \, t \hspace{2em} y( 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?{y} = -t + \frac{4}{t^{4}}" alt="{y} = -t + \frac{4}{t^{4}}" title="{y} = -t + \frac{4}{t^{4}}" data-latex="{y} = -t + \frac{4}{t^{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?%7By%7D%20=%20-t%20+%20%5Cfrac%7B4%7D%7Bt%5E%7B4%7D%7D" alt="{y} = -t + \frac{4}{t^{4}}" title="{y} = -t + \frac{4}{t^{4}}" data-latex="{y} = -t + \frac{4}{t^{4}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-0549" title="F3 | Techniques for linear IVPs | ver. 0549"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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 + 4 \, {y} = 35 \, t^{3} \hspace{2em} y( -1 )= -9" alt="{y'} t + 4 \, {y} = 35 \, t^{3} \hspace{2em} y( -1 )= -9" title="{y'} t + 4 \, {y} = 35 \, t^{3} \hspace{2em} y( -1 )= -9" data-latex="{y'} t + 4 \, {y} = 35 \, t^{3} \hspace{2em} y( -1 )= -9"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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+%204%20%5C,%20%7By%7D%20=%2035%20%5C,%20t%5E%7B3%7D%20%5Chspace%7B2em%7D%20y(%20-1%20)=%20-9" alt="{y'} t + 4 \, {y} = 35 \, t^{3} \hspace{2em} y( -1 )= -9" title="{y'} t + 4 \, {y} = 35 \, t^{3} \hspace{2em} y( -1 )= -9" data-latex="{y'} t + 4 \, {y} = 35 \, t^{3} \hspace{2em} y( -1 )= -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?{y} = 5 \, t^{3} - \frac{4}{t^{4}}" alt="{y} = 5 \, t^{3} - \frac{4}{t^{4}}" title="{y} = 5 \, t^{3} - \frac{4}{t^{4}}" data-latex="{y} = 5 \, t^{3} - \frac{4}{t^{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?%7By%7D%20=%205%20%5C,%20t%5E%7B3%7D%20-%20%5Cfrac%7B4%7D%7Bt%5E%7B4%7D%7D" alt="{y} = 5 \, t^{3} - \frac{4}{t^{4}}" title="{y} = 5 \, t^{3} - \frac{4}{t^{4}}" data-latex="{y} = 5 \, t^{3} - \frac{4}{t^{4}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-9462" title="F3 | Techniques for linear IVPs | ver. 9462"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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 + 3 \, {y} = -35 \, t^{4} \hspace{2em} y( 1 )= -1" alt="{y'} t + 3 \, {y} = -35 \, t^{4} \hspace{2em} y( 1 )= -1" title="{y'} t + 3 \, {y} = -35 \, t^{4} \hspace{2em} y( 1 )= -1" data-latex="{y'} t + 3 \, {y} = -35 \, t^{4} \hspace{2em} y( 1 )= -1"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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+%203%20%5C,%20%7By%7D%20=%20-35%20%5C,%20t%5E%7B4%7D%20%5Chspace%7B2em%7D%20y(%201%20)=%20-1" alt="{y'} t + 3 \, {y} = -35 \, t^{4} \hspace{2em} y( 1 )= -1" title="{y'} t + 3 \, {y} = -35 \, t^{4} \hspace{2em} y( 1 )= -1" data-latex="{y'} t + 3 \, {y} = -35 \, t^{4} \hspace{2em} y( 1 )= -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?{y} = -5 \, t^{4} + \frac{4}{t^{3}}" alt="{y} = -5 \, t^{4} + \frac{4}{t^{3}}" title="{y} = -5 \, t^{4} + \frac{4}{t^{3}}" data-latex="{y} = -5 \, t^{4} + \frac{4}{t^{3}}"/></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?%7By%7D%20=%20-5%20%5C,%20t%5E%7B4%7D%20+%20%5Cfrac%7B4%7D%7Bt%5E%7B3%7D%7D" alt="{y} = -5 \, t^{4} + \frac{4}{t^{3}}" title="{y} = -5 \, t^{4} + \frac{4}{t^{3}}" data-latex="{y} = -5 \, t^{4} + \frac{4}{t^{3}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-1542" title="F3 | Techniques for linear IVPs | ver. 1542"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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 - \frac{15}{t^{3}} = 2 \, {y} \hspace{2em} y( -1 )= 7" alt="{y'} t - \frac{15}{t^{3}} = 2 \, {y} \hspace{2em} y( -1 )= 7" title="{y'} t - \frac{15}{t^{3}} = 2 \, {y} \hspace{2em} y( -1 )= 7" data-latex="{y'} t - \frac{15}{t^{3}} = 2 \, {y} \hspace{2em} y( -1 )= 7"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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%5Cfrac%7B15%7D%7Bt%5E%7B3%7D%7D%20=%202%20%5C,%20%7By%7D%20%5Chspace%7B2em%7D%20y(%20-1%20)=%207" alt="{y'} t - \frac{15}{t^{3}} = 2 \, {y} \hspace{2em} y( -1 )= 7" title="{y'} t - \frac{15}{t^{3}} = 2 \, {y} \hspace{2em} y( -1 )= 7" data-latex="{y'} t - \frac{15}{t^{3}} = 2 \, {y} \hspace{2em} y( -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?{y} = 4 \, t^{2} - \frac{3}{t^{3}}" alt="{y} = 4 \, t^{2} - \frac{3}{t^{3}}" title="{y} = 4 \, t^{2} - \frac{3}{t^{3}}" data-latex="{y} = 4 \, t^{2} - \frac{3}{t^{3}}"/></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?%7By%7D%20=%204%20%5C,%20t%5E%7B2%7D%20-%20%5Cfrac%7B3%7D%7Bt%5E%7B3%7D%7D" alt="{y} = 4 \, t^{2} - \frac{3}{t^{3}}" title="{y} = 4 \, t^{2} - \frac{3}{t^{3}}" data-latex="{y} = 4 \, t^{2} - \frac{3}{t^{3}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-5446" title="F3 | Techniques for linear IVPs | ver. 5446"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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?-35 \, t^{2} - 5 \, {y} = t {y'} \hspace{2em} y( -1 )= -2" alt="-35 \, t^{2} - 5 \, {y} = t {y'} \hspace{2em} y( -1 )= -2" title="-35 \, t^{2} - 5 \, {y} = t {y'} \hspace{2em} y( -1 )= -2" data-latex="-35 \, t^{2} - 5 \, {y} = t {y'} \hspace{2em} y( -1 )= -2"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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?-35%20%5C,%20t%5E%7B2%7D%20-%205%20%5C,%20%7By%7D%20=%20t%20%7By'%7D%20%5Chspace%7B2em%7D%20y(%20-1%20)=%20-2" alt="-35 \, t^{2} - 5 \, {y} = t {y'} \hspace{2em} y( -1 )= -2" title="-35 \, t^{2} - 5 \, {y} = t {y'} \hspace{2em} y( -1 )= -2" data-latex="-35 \, t^{2} - 5 \, {y} = t {y'} \hspace{2em} y( -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?{y} = -5 \, t^{2} - \frac{3}{t^{5}}" alt="{y} = -5 \, t^{2} - \frac{3}{t^{5}}" title="{y} = -5 \, t^{2} - \frac{3}{t^{5}}" data-latex="{y} = -5 \, t^{2} - \frac{3}{t^{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?%7By%7D%20=%20-5%20%5C,%20t%5E%7B2%7D%20-%20%5Cfrac%7B3%7D%7Bt%5E%7B5%7D%7D" alt="{y} = -5 \, t^{2} - \frac{3}{t^{5}}" title="{y} = -5 \, t^{2} - \frac{3}{t^{5}}" data-latex="{y} = -5 \, t^{2} - \frac{3}{t^{5}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-6949" title="F3 | Techniques for linear IVPs | ver. 6949"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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 + 2 \, {y} + \frac{16}{t^{2}} = 0 \hspace{2em} y( 1 )= -7" alt="-{y'} t + 2 \, {y} + \frac{16}{t^{2}} = 0 \hspace{2em} y( 1 )= -7" title="-{y'} t + 2 \, {y} + \frac{16}{t^{2}} = 0 \hspace{2em} y( 1 )= -7" data-latex="-{y'} t + 2 \, {y} + \frac{16}{t^{2}} = 0 \hspace{2em} y( 1 )= -7"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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+%202%20%5C,%20%7By%7D%20+%20%5Cfrac%7B16%7D%7Bt%5E%7B2%7D%7D%20=%200%20%5Chspace%7B2em%7D%20y(%201%20)=%20-7" alt="-{y'} t + 2 \, {y} + \frac{16}{t^{2}} = 0 \hspace{2em} y( 1 )= -7" title="-{y'} t + 2 \, {y} + \frac{16}{t^{2}} = 0 \hspace{2em} y( 1 )= -7" data-latex="-{y'} t + 2 \, {y} + \frac{16}{t^{2}} = 0 \hspace{2em} y( 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?{y} = -3 \, t^{2} - \frac{4}{t^{2}}" alt="{y} = -3 \, t^{2} - \frac{4}{t^{2}}" title="{y} = -3 \, t^{2} - \frac{4}{t^{2}}" data-latex="{y} = -3 \, t^{2} - \frac{4}{t^{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?%7By%7D%20=%20-3%20%5C,%20t%5E%7B2%7D%20-%20%5Cfrac%7B4%7D%7Bt%5E%7B2%7D%7D" alt="{y} = -3 \, t^{2} - \frac{4}{t^{2}}" title="{y} = -3 \, t^{2} - \frac{4}{t^{2}}" data-latex="{y} = -3 \, t^{2} - \frac{4}{t^{2}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-8520" title="F3 | Techniques for linear IVPs | ver. 8520"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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 = 24 \, t^{3} + 5 \, {y} \hspace{2em} y( -1 )= 0" alt="-{y'} t = 24 \, t^{3} + 5 \, {y} \hspace{2em} y( -1 )= 0" title="-{y'} t = 24 \, t^{3} + 5 \, {y} \hspace{2em} y( -1 )= 0" data-latex="-{y'} t = 24 \, t^{3} + 5 \, {y} \hspace{2em} y( -1 )= 0"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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=%2024%20%5C,%20t%5E%7B3%7D%20+%205%20%5C,%20%7By%7D%20%5Chspace%7B2em%7D%20y(%20-1%20)=%200" alt="-{y'} t = 24 \, t^{3} + 5 \, {y} \hspace{2em} y( -1 )= 0" title="-{y'} t = 24 \, t^{3} + 5 \, {y} \hspace{2em} y( -1 )= 0" data-latex="-{y'} t = 24 \, t^{3} + 5 \, {y} \hspace{2em} y( -1 )= 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?{y} = -3 \, t^{3} + \frac{3}{t^{5}}" alt="{y} = -3 \, t^{3} + \frac{3}{t^{5}}" title="{y} = -3 \, t^{3} + \frac{3}{t^{5}}" data-latex="{y} = -3 \, t^{3} + \frac{3}{t^{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?%7By%7D%20=%20-3%20%5C,%20t%5E%7B3%7D%20+%20%5Cfrac%7B3%7D%7Bt%5E%7B5%7D%7D" alt="{y} = -3 \, t^{3} + \frac{3}{t^{5}}" title="{y} = -3 \, t^{3} + \frac{3}{t^{5}}" data-latex="{y} = -3 \, t^{3} + \frac{3}{t^{5}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-4261" title="F3 | Techniques for linear IVPs | ver. 4261"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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 = 5 \, {y} + 6 \, t \hspace{2em} y( -1 )= 3" alt="-{y'} t = 5 \, {y} + 6 \, t \hspace{2em} y( -1 )= 3" title="-{y'} t = 5 \, {y} + 6 \, t \hspace{2em} y( -1 )= 3" data-latex="-{y'} t = 5 \, {y} + 6 \, t \hspace{2em} y( -1 )= 3"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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=%205%20%5C,%20%7By%7D%20+%206%20%5C,%20t%20%5Chspace%7B2em%7D%20y(%20-1%20)=%203" alt="-{y'} t = 5 \, {y} + 6 \, t \hspace{2em} y( -1 )= 3" title="-{y'} t = 5 \, {y} + 6 \, t \hspace{2em} y( -1 )= 3" data-latex="-{y'} t = 5 \, {y} + 6 \, t \hspace{2em} y( -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?{y} = -t - \frac{2}{t^{5}}" alt="{y} = -t - \frac{2}{t^{5}}" title="{y} = -t - \frac{2}{t^{5}}" data-latex="{y} = -t - \frac{2}{t^{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?%7By%7D%20=%20-t%20-%20%5Cfrac%7B2%7D%7Bt%5E%7B5%7D%7D" alt="{y} = -t - \frac{2}{t^{5}}" title="{y} = -t - \frac{2}{t^{5}}" data-latex="{y} = -t - \frac{2}{t^{5}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-3835" title="F3 | Techniques for linear IVPs | ver. 3835"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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'} t + 2 \, {y} - 3 \, t \hspace{2em} y( 1 )= -1" alt="0 = -{y'} t + 2 \, {y} - 3 \, t \hspace{2em} y( 1 )= -1" title="0 = -{y'} t + 2 \, {y} - 3 \, t \hspace{2em} y( 1 )= -1" data-latex="0 = -{y'} t + 2 \, {y} - 3 \, t \hspace{2em} y( 1 )= -1"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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%20t%20+%202%20%5C,%20%7By%7D%20-%203%20%5C,%20t%20%5Chspace%7B2em%7D%20y(%201%20)=%20-1" alt="0 = -{y'} t + 2 \, {y} - 3 \, t \hspace{2em} y( 1 )= -1" title="0 = -{y'} t + 2 \, {y} - 3 \, t \hspace{2em} y( 1 )= -1" data-latex="0 = -{y'} t + 2 \, {y} - 3 \, t \hspace{2em} y( 1 )= -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?{y} = -4 \, t^{2} + 3 \, t" alt="{y} = -4 \, t^{2} + 3 \, t" title="{y} = -4 \, t^{2} + 3 \, t" data-latex="{y} = -4 \, t^{2} + 3 \, t"/></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?%7By%7D%20=%20-4%20%5C,%20t%5E%7B2%7D%20+%203%20%5C,%20t" alt="{y} = -4 \, t^{2} + 3 \, t" title="{y} = -4 \, t^{2} + 3 \, t" data-latex="{y} = -4 \, t^{2} + 3 \, t"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-5872" title="F3 | Techniques for linear IVPs | ver. 5872"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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?-\frac{7}{t^{2}} = -t {y'} + 5 \, {y} \hspace{2em} y( -1 )= -4" alt="-\frac{7}{t^{2}} = -t {y'} + 5 \, {y} \hspace{2em} y( -1 )= -4" title="-\frac{7}{t^{2}} = -t {y'} + 5 \, {y} \hspace{2em} y( -1 )= -4" data-latex="-\frac{7}{t^{2}} = -t {y'} + 5 \, {y} \hspace{2em} y( -1 )= -4"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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?-%5Cfrac%7B7%7D%7Bt%5E%7B2%7D%7D%20=%20-t%20%7By'%7D%20+%205%20%5C,%20%7By%7D%20%5Chspace%7B2em%7D%20y(%20-1%20)=%20-4" alt="-\frac{7}{t^{2}} = -t {y'} + 5 \, {y} \hspace{2em} y( -1 )= -4" title="-\frac{7}{t^{2}} = -t {y'} + 5 \, {y} \hspace{2em} y( -1 )= -4" data-latex="-\frac{7}{t^{2}} = -t {y'} + 5 \, {y} \hspace{2em} y( -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?{y} = 3 \, t^{5} - \frac{1}{t^{2}}" alt="{y} = 3 \, t^{5} - \frac{1}{t^{2}}" title="{y} = 3 \, t^{5} - \frac{1}{t^{2}}" data-latex="{y} = 3 \, t^{5} - \frac{1}{t^{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?%7By%7D%20=%203%20%5C,%20t%5E%7B5%7D%20-%20%5Cfrac%7B1%7D%7Bt%5E%7B2%7D%7D" alt="{y} = 3 \, t^{5} - \frac{1}{t^{2}}" title="{y} = 3 \, t^{5} - \frac{1}{t^{2}}" data-latex="{y} = 3 \, t^{5} - \frac{1}{t^{2}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-2794" title="F3 | Techniques for linear IVPs | ver. 2794"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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 - 2 \, {y} + \frac{1}{t^{3}} = 0 \hspace{2em} y( -1 )= -1" alt="-{y'} t - 2 \, {y} + \frac{1}{t^{3}} = 0 \hspace{2em} y( -1 )= -1" title="-{y'} t - 2 \, {y} + \frac{1}{t^{3}} = 0 \hspace{2em} y( -1 )= -1" data-latex="-{y'} t - 2 \, {y} + \frac{1}{t^{3}} = 0 \hspace{2em} y( -1 )= -1"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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-%202%20%5C,%20%7By%7D%20+%20%5Cfrac%7B1%7D%7Bt%5E%7B3%7D%7D%20=%200%20%5Chspace%7B2em%7D%20y(%20-1%20)=%20-1" alt="-{y'} t - 2 \, {y} + \frac{1}{t^{3}} = 0 \hspace{2em} y( -1 )= -1" title="-{y'} t - 2 \, {y} + \frac{1}{t^{3}} = 0 \hspace{2em} y( -1 )= -1" data-latex="-{y'} t - 2 \, {y} + \frac{1}{t^{3}} = 0 \hspace{2em} y( -1 )= -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?{y} = -\frac{2}{t^{2}} - \frac{1}{t^{3}}" alt="{y} = -\frac{2}{t^{2}} - \frac{1}{t^{3}}" title="{y} = -\frac{2}{t^{2}} - \frac{1}{t^{3}}" data-latex="{y} = -\frac{2}{t^{2}} - \frac{1}{t^{3}}"/></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?%7By%7D%20=%20-%5Cfrac%7B2%7D%7Bt%5E%7B2%7D%7D%20-%20%5Cfrac%7B1%7D%7Bt%5E%7B3%7D%7D" alt="{y} = -\frac{2}{t^{2}} - \frac{1}{t^{3}}" title="{y} = -\frac{2}{t^{2}} - \frac{1}{t^{3}}" data-latex="{y} = -\frac{2}{t^{2}} - \frac{1}{t^{3}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-3105" title="F3 | Techniques for linear IVPs | ver. 3105"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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?-\frac{6}{t^{2}} = {y'} t + 4 \, {y} \hspace{2em} y( 1 )= -2" alt="-\frac{6}{t^{2}} = {y'} t + 4 \, {y} \hspace{2em} y( 1 )= -2" title="-\frac{6}{t^{2}} = {y'} t + 4 \, {y} \hspace{2em} y( 1 )= -2" data-latex="-\frac{6}{t^{2}} = {y'} t + 4 \, {y} \hspace{2em} y( 1 )= -2"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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?-%5Cfrac%7B6%7D%7Bt%5E%7B2%7D%7D%20=%20%7By'%7D%20t%20+%204%20%5C,%20%7By%7D%20%5Chspace%7B2em%7D%20y(%201%20)=%20-2" alt="-\frac{6}{t^{2}} = {y'} t + 4 \, {y} \hspace{2em} y( 1 )= -2" title="-\frac{6}{t^{2}} = {y'} t + 4 \, {y} \hspace{2em} y( 1 )= -2" data-latex="-\frac{6}{t^{2}} = {y'} t + 4 \, {y} \hspace{2em} y( 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?{y} = -\frac{3}{t^{2}} + \frac{1}{t^{4}}" alt="{y} = -\frac{3}{t^{2}} + \frac{1}{t^{4}}" title="{y} = -\frac{3}{t^{2}} + \frac{1}{t^{4}}" data-latex="{y} = -\frac{3}{t^{2}} + \frac{1}{t^{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?%7By%7D%20=%20-%5Cfrac%7B3%7D%7Bt%5E%7B2%7D%7D%20+%20%5Cfrac%7B1%7D%7Bt%5E%7B4%7D%7D" alt="{y} = -\frac{3}{t^{2}} + \frac{1}{t^{4}}" title="{y} = -\frac{3}{t^{2}} + \frac{1}{t^{4}}" data-latex="{y} = -\frac{3}{t^{2}} + \frac{1}{t^{4}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-9806" title="F3 | Techniques for linear IVPs | ver. 9806"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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 {y'} + 4 \, {y} - \frac{6}{t^{2}} = 0 \hspace{2em} y( 1 )= 4" alt="-t {y'} + 4 \, {y} - \frac{6}{t^{2}} = 0 \hspace{2em} y( 1 )= 4" title="-t {y'} + 4 \, {y} - \frac{6}{t^{2}} = 0 \hspace{2em} y( 1 )= 4" data-latex="-t {y'} + 4 \, {y} - \frac{6}{t^{2}} = 0 \hspace{2em} y( 1 )= 4"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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%7By'%7D%20+%204%20%5C,%20%7By%7D%20-%20%5Cfrac%7B6%7D%7Bt%5E%7B2%7D%7D%20=%200%20%5Chspace%7B2em%7D%20y(%201%20)=%204" alt="-t {y'} + 4 \, {y} - \frac{6}{t^{2}} = 0 \hspace{2em} y( 1 )= 4" title="-t {y'} + 4 \, {y} - \frac{6}{t^{2}} = 0 \hspace{2em} y( 1 )= 4" data-latex="-t {y'} + 4 \, {y} - \frac{6}{t^{2}} = 0 \hspace{2em} y( 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?{y} = 3 \, t^{4} + \frac{1}{t^{2}}" alt="{y} = 3 \, t^{4} + \frac{1}{t^{2}}" title="{y} = 3 \, t^{4} + \frac{1}{t^{2}}" data-latex="{y} = 3 \, t^{4} + \frac{1}{t^{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?%7By%7D%20=%203%20%5C,%20t%5E%7B4%7D%20+%20%5Cfrac%7B1%7D%7Bt%5E%7B2%7D%7D" alt="{y} = 3 \, t^{4} + \frac{1}{t^{2}}" title="{y} = 3 \, t^{4} + \frac{1}{t^{2}}" data-latex="{y} = 3 \, t^{4} + \frac{1}{t^{2}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-6044" title="F3 | Techniques for linear IVPs | ver. 6044"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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?6 \, t^{4} = {y'} t - 2 \, {y} \hspace{2em} y( -1 )= -1" alt="6 \, t^{4} = {y'} t - 2 \, {y} \hspace{2em} y( -1 )= -1" title="6 \, t^{4} = {y'} t - 2 \, {y} \hspace{2em} y( -1 )= -1" data-latex="6 \, t^{4} = {y'} t - 2 \, {y} \hspace{2em} y( -1 )= -1"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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?6%20%5C,%20t%5E%7B4%7D%20=%20%7By'%7D%20t%20-%202%20%5C,%20%7By%7D%20%5Chspace%7B2em%7D%20y(%20-1%20)=%20-1" alt="6 \, t^{4} = {y'} t - 2 \, {y} \hspace{2em} y( -1 )= -1" title="6 \, t^{4} = {y'} t - 2 \, {y} \hspace{2em} y( -1 )= -1" data-latex="6 \, t^{4} = {y'} t - 2 \, {y} \hspace{2em} y( -1 )= -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?{y} = 3 \, t^{4} - 4 \, t^{2}" alt="{y} = 3 \, t^{4} - 4 \, t^{2}" title="{y} = 3 \, t^{4} - 4 \, t^{2}" data-latex="{y} = 3 \, t^{4} - 4 \, t^{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?%7By%7D%20=%203%20%5C,%20t%5E%7B4%7D%20-%204%20%5C,%20t%5E%7B2%7D" alt="{y} = 3 \, t^{4} - 4 \, t^{2}" title="{y} = 3 \, t^{4} - 4 \, t^{2}" data-latex="{y} = 3 \, t^{4} - 4 \, t^{2}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-1065" title="F3 | Techniques for linear IVPs | ver. 1065"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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 + 2 \, t^{2} = -4 \, {y} \hspace{2em} y( 1 )= -5" alt="-{y'} t + 2 \, t^{2} = -4 \, {y} \hspace{2em} y( 1 )= -5" title="-{y'} t + 2 \, t^{2} = -4 \, {y} \hspace{2em} y( 1 )= -5" data-latex="-{y'} t + 2 \, t^{2} = -4 \, {y} \hspace{2em} y( 1 )= -5"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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+%202%20%5C,%20t%5E%7B2%7D%20=%20-4%20%5C,%20%7By%7D%20%5Chspace%7B2em%7D%20y(%201%20)=%20-5" alt="-{y'} t + 2 \, t^{2} = -4 \, {y} \hspace{2em} y( 1 )= -5" title="-{y'} t + 2 \, t^{2} = -4 \, {y} \hspace{2em} y( 1 )= -5" data-latex="-{y'} t + 2 \, t^{2} = -4 \, {y} \hspace{2em} y( 1 )= -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?{y} = -4 \, t^{4} - t^{2}" alt="{y} = -4 \, t^{4} - t^{2}" title="{y} = -4 \, t^{4} - t^{2}" data-latex="{y} = -4 \, t^{4} - t^{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?%7By%7D%20=%20-4%20%5C,%20t%5E%7B4%7D%20-%20t%5E%7B2%7D" alt="{y} = -4 \, t^{4} - t^{2}" title="{y} = -4 \, t^{4} - t^{2}" data-latex="{y} = -4 \, t^{4} - t^{2}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-3305" title="F3 | Techniques for linear IVPs | ver. 3305"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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?-3 \, {y} = -{y'} t + \frac{18}{t^{3}} \hspace{2em} y( -1 )= -1" alt="-3 \, {y} = -{y'} t + \frac{18}{t^{3}} \hspace{2em} y( -1 )= -1" title="-3 \, {y} = -{y'} t + \frac{18}{t^{3}} \hspace{2em} y( -1 )= -1" data-latex="-3 \, {y} = -{y'} t + \frac{18}{t^{3}} \hspace{2em} y( -1 )= -1"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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?-3%20%5C,%20%7By%7D%20=%20-%7By'%7D%20t%20+%20%5Cfrac%7B18%7D%7Bt%5E%7B3%7D%7D%20%5Chspace%7B2em%7D%20y(%20-1%20)=%20-1" alt="-3 \, {y} = -{y'} t + \frac{18}{t^{3}} \hspace{2em} y( -1 )= -1" title="-3 \, {y} = -{y'} t + \frac{18}{t^{3}} \hspace{2em} y( -1 )= -1" data-latex="-3 \, {y} = -{y'} t + \frac{18}{t^{3}} \hspace{2em} y( -1 )= -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?{y} = 4 \, t^{3} - \frac{3}{t^{3}}" alt="{y} = 4 \, t^{3} - \frac{3}{t^{3}}" title="{y} = 4 \, t^{3} - \frac{3}{t^{3}}" data-latex="{y} = 4 \, t^{3} - \frac{3}{t^{3}}"/></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?%7By%7D%20=%204%20%5C,%20t%5E%7B3%7D%20-%20%5Cfrac%7B3%7D%7Bt%5E%7B3%7D%7D" alt="{y} = 4 \, t^{3} - \frac{3}{t^{3}}" title="{y} = 4 \, t^{3} - \frac{3}{t^{3}}" data-latex="{y} = 4 \, t^{3} - \frac{3}{t^{3}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-9067" title="F3 | Techniques for linear IVPs | ver. 9067"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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 + 2 \, {y} + 4 \, t = 0 \hspace{2em} y( -1 )= 6" alt="-{y'} t + 2 \, {y} + 4 \, t = 0 \hspace{2em} y( -1 )= 6" title="-{y'} t + 2 \, {y} + 4 \, t = 0 \hspace{2em} y( -1 )= 6" data-latex="-{y'} t + 2 \, {y} + 4 \, t = 0 \hspace{2em} y( -1 )= 6"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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+%202%20%5C,%20%7By%7D%20+%204%20%5C,%20t%20=%200%20%5Chspace%7B2em%7D%20y(%20-1%20)=%206" alt="-{y'} t + 2 \, {y} + 4 \, t = 0 \hspace{2em} y( -1 )= 6" title="-{y'} t + 2 \, {y} + 4 \, t = 0 \hspace{2em} y( -1 )= 6" data-latex="-{y'} t + 2 \, {y} + 4 \, t = 0 \hspace{2em} y( -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?{y} = 2 \, t^{2} - 4 \, t" alt="{y} = 2 \, t^{2} - 4 \, t" title="{y} = 2 \, t^{2} - 4 \, t" data-latex="{y} = 2 \, t^{2} - 4 \, t"/></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?%7By%7D%20=%202%20%5C,%20t%5E%7B2%7D%20-%204%20%5C,%20t" alt="{y} = 2 \, t^{2} - 4 \, t" title="{y} = 2 \, t^{2} - 4 \, t" data-latex="{y} = 2 \, t^{2} - 4 \, t"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-2293" title="F3 | Techniques for linear IVPs | ver. 2293"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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?35 \, t^{4} - t {y'} - 3 \, {y} = 0 \hspace{2em} y( 1 )= 2" alt="35 \, t^{4} - t {y'} - 3 \, {y} = 0 \hspace{2em} y( 1 )= 2" title="35 \, t^{4} - t {y'} - 3 \, {y} = 0 \hspace{2em} y( 1 )= 2" data-latex="35 \, t^{4} - t {y'} - 3 \, {y} = 0 \hspace{2em} y( 1 )= 2"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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?35%20%5C,%20t%5E%7B4%7D%20-%20t%20%7By'%7D%20-%203%20%5C,%20%7By%7D%20=%200%20%5Chspace%7B2em%7D%20y(%201%20)=%202" alt="35 \, t^{4} - t {y'} - 3 \, {y} = 0 \hspace{2em} y( 1 )= 2" title="35 \, t^{4} - t {y'} - 3 \, {y} = 0 \hspace{2em} y( 1 )= 2" data-latex="35 \, t^{4} - t {y'} - 3 \, {y} = 0 \hspace{2em} y( 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?{y} = 5 \, t^{4} - \frac{3}{t^{3}}" alt="{y} = 5 \, t^{4} - \frac{3}{t^{3}}" title="{y} = 5 \, t^{4} - \frac{3}{t^{3}}" data-latex="{y} = 5 \, t^{4} - \frac{3}{t^{3}}"/></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?%7By%7D%20=%205%20%5C,%20t%5E%7B4%7D%20-%20%5Cfrac%7B3%7D%7Bt%5E%7B3%7D%7D" alt="{y} = 5 \, t^{4} - \frac{3}{t^{3}}" title="{y} = 5 \, t^{4} - \frac{3}{t^{3}}" data-latex="{y} = 5 \, t^{4} - \frac{3}{t^{3}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-1549" title="F3 | Techniques for linear IVPs | ver. 1549"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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'} t + 3 \, {y} + 20 \, t \hspace{2em} y( 1 )= -3" alt="0 = {y'} t + 3 \, {y} + 20 \, t \hspace{2em} y( 1 )= -3" title="0 = {y'} t + 3 \, {y} + 20 \, t \hspace{2em} y( 1 )= -3" data-latex="0 = {y'} t + 3 \, {y} + 20 \, t \hspace{2em} y( 1 )= -3"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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%20t%20+%203%20%5C,%20%7By%7D%20+%2020%20%5C,%20t%20%5Chspace%7B2em%7D%20y(%201%20)=%20-3" alt="0 = {y'} t + 3 \, {y} + 20 \, t \hspace{2em} y( 1 )= -3" title="0 = {y'} t + 3 \, {y} + 20 \, t \hspace{2em} y( 1 )= -3" data-latex="0 = {y'} t + 3 \, {y} + 20 \, t \hspace{2em} y( 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?{y} = -5 \, t + \frac{2}{t^{3}}" alt="{y} = -5 \, t + \frac{2}{t^{3}}" title="{y} = -5 \, t + \frac{2}{t^{3}}" data-latex="{y} = -5 \, t + \frac{2}{t^{3}}"/></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?%7By%7D%20=%20-5%20%5C,%20t%20+%20%5Cfrac%7B2%7D%7Bt%5E%7B3%7D%7D" alt="{y} = -5 \, t + \frac{2}{t^{3}}" title="{y} = -5 \, t + \frac{2}{t^{3}}" data-latex="{y} = -5 \, t + \frac{2}{t^{3}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-3148" title="F3 | Techniques for linear IVPs | ver. 3148"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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 = -3 \, {y} + 20 \, t \hspace{2em} y( -1 )= -9" alt="{y'} t = -3 \, {y} + 20 \, t \hspace{2em} y( -1 )= -9" title="{y'} t = -3 \, {y} + 20 \, t \hspace{2em} y( -1 )= -9" data-latex="{y'} t = -3 \, {y} + 20 \, t \hspace{2em} y( -1 )= -9"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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=%20-3%20%5C,%20%7By%7D%20+%2020%20%5C,%20t%20%5Chspace%7B2em%7D%20y(%20-1%20)=%20-9" alt="{y'} t = -3 \, {y} + 20 \, t \hspace{2em} y( -1 )= -9" title="{y'} t = -3 \, {y} + 20 \, t \hspace{2em} y( -1 )= -9" data-latex="{y'} t = -3 \, {y} + 20 \, t \hspace{2em} y( -1 )= -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?{y} = 5 \, t + \frac{4}{t^{3}}" alt="{y} = 5 \, t + \frac{4}{t^{3}}" title="{y} = 5 \, t + \frac{4}{t^{3}}" data-latex="{y} = 5 \, t + \frac{4}{t^{3}}"/></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?%7By%7D%20=%205%20%5C,%20t%20+%20%5Cfrac%7B4%7D%7Bt%5E%7B3%7D%7D" alt="{y} = 5 \, t + \frac{4}{t^{3}}" title="{y} = 5 \, t + \frac{4}{t^{3}}" data-latex="{y} = 5 \, t + \frac{4}{t^{3}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-4885" title="F3 | Techniques for linear IVPs | ver. 4885"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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?-\frac{6}{t^{3}} = -t {y'} - 5 \, {y} \hspace{2em} y( 1 )= 4" alt="-\frac{6}{t^{3}} = -t {y'} - 5 \, {y} \hspace{2em} y( 1 )= 4" title="-\frac{6}{t^{3}} = -t {y'} - 5 \, {y} \hspace{2em} y( 1 )= 4" data-latex="-\frac{6}{t^{3}} = -t {y'} - 5 \, {y} \hspace{2em} y( 1 )= 4"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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?-%5Cfrac%7B6%7D%7Bt%5E%7B3%7D%7D%20=%20-t%20%7By'%7D%20-%205%20%5C,%20%7By%7D%20%5Chspace%7B2em%7D%20y(%201%20)=%204" alt="-\frac{6}{t^{3}} = -t {y'} - 5 \, {y} \hspace{2em} y( 1 )= 4" title="-\frac{6}{t^{3}} = -t {y'} - 5 \, {y} \hspace{2em} y( 1 )= 4" data-latex="-\frac{6}{t^{3}} = -t {y'} - 5 \, {y} \hspace{2em} y( 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?{y} = \frac{3}{t^{3}} + \frac{1}{t^{5}}" alt="{y} = \frac{3}{t^{3}} + \frac{1}{t^{5}}" title="{y} = \frac{3}{t^{3}} + \frac{1}{t^{5}}" data-latex="{y} = \frac{3}{t^{3}} + \frac{1}{t^{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?%7By%7D%20=%20%5Cfrac%7B3%7D%7Bt%5E%7B3%7D%7D%20+%20%5Cfrac%7B1%7D%7Bt%5E%7B5%7D%7D" alt="{y} = \frac{3}{t^{3}} + \frac{1}{t^{5}}" title="{y} = \frac{3}{t^{3}} + \frac{1}{t^{5}}" data-latex="{y} = \frac{3}{t^{3}} + \frac{1}{t^{5}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-8890" title="F3 | Techniques for linear IVPs | ver. 8890"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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'} t + 3 \, {y} + 6 \, t \hspace{2em} y( 1 )= -1" alt="0 = -{y'} t + 3 \, {y} + 6 \, t \hspace{2em} y( 1 )= -1" title="0 = -{y'} t + 3 \, {y} + 6 \, t \hspace{2em} y( 1 )= -1" data-latex="0 = -{y'} t + 3 \, {y} + 6 \, t \hspace{2em} y( 1 )= -1"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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%20t%20+%203%20%5C,%20%7By%7D%20+%206%20%5C,%20t%20%5Chspace%7B2em%7D%20y(%201%20)=%20-1" alt="0 = -{y'} t + 3 \, {y} + 6 \, t \hspace{2em} y( 1 )= -1" title="0 = -{y'} t + 3 \, {y} + 6 \, t \hspace{2em} y( 1 )= -1" data-latex="0 = -{y'} t + 3 \, {y} + 6 \, t \hspace{2em} y( 1 )= -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?{y} = 2 \, t^{3} - 3 \, t" alt="{y} = 2 \, t^{3} - 3 \, t" title="{y} = 2 \, t^{3} - 3 \, t" data-latex="{y} = 2 \, t^{3} - 3 \, t"/></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?%7By%7D%20=%202%20%5C,%20t%5E%7B3%7D%20-%203%20%5C,%20t" alt="{y} = 2 \, t^{3} - 3 \, t" title="{y} = 2 \, t^{3} - 3 \, t" data-latex="{y} = 2 \, t^{3} - 3 \, t"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-0492" title="F3 | Techniques for linear IVPs | ver. 0492"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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?3 \, {y} + \frac{7}{t^{4}} = {y'} t \hspace{2em} y( 1 )= -2" alt="3 \, {y} + \frac{7}{t^{4}} = {y'} t \hspace{2em} y( 1 )= -2" title="3 \, {y} + \frac{7}{t^{4}} = {y'} t \hspace{2em} y( 1 )= -2" data-latex="3 \, {y} + \frac{7}{t^{4}} = {y'} t \hspace{2em} y( 1 )= -2"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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?3%20%5C,%20%7By%7D%20+%20%5Cfrac%7B7%7D%7Bt%5E%7B4%7D%7D%20=%20%7By'%7D%20t%20%5Chspace%7B2em%7D%20y(%201%20)=%20-2" alt="3 \, {y} + \frac{7}{t^{4}} = {y'} t \hspace{2em} y( 1 )= -2" title="3 \, {y} + \frac{7}{t^{4}} = {y'} t \hspace{2em} y( 1 )= -2" data-latex="3 \, {y} + \frac{7}{t^{4}} = {y'} t \hspace{2em} y( 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?{y} = -t^{3} - \frac{1}{t^{4}}" alt="{y} = -t^{3} - \frac{1}{t^{4}}" title="{y} = -t^{3} - \frac{1}{t^{4}}" data-latex="{y} = -t^{3} - \frac{1}{t^{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?%7By%7D%20=%20-t%5E%7B3%7D%20-%20%5Cfrac%7B1%7D%7Bt%5E%7B4%7D%7D" alt="{y} = -t^{3} - \frac{1}{t^{4}}" title="{y} = -t^{3} - \frac{1}{t^{4}}" data-latex="{y} = -t^{3} - \frac{1}{t^{4}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-1587" title="F3 | Techniques for linear IVPs | ver. 1587"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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?3 \, {y} = 4 \, t^{4} + {y'} t \hspace{2em} y( 1 )= -2" alt="3 \, {y} = 4 \, t^{4} + {y'} t \hspace{2em} y( 1 )= -2" title="3 \, {y} = 4 \, t^{4} + {y'} t \hspace{2em} y( 1 )= -2" data-latex="3 \, {y} = 4 \, t^{4} + {y'} t \hspace{2em} y( 1 )= -2"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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?3%20%5C,%20%7By%7D%20=%204%20%5C,%20t%5E%7B4%7D%20+%20%7By'%7D%20t%20%5Chspace%7B2em%7D%20y(%201%20)=%20-2" alt="3 \, {y} = 4 \, t^{4} + {y'} t \hspace{2em} y( 1 )= -2" title="3 \, {y} = 4 \, t^{4} + {y'} t \hspace{2em} y( 1 )= -2" data-latex="3 \, {y} = 4 \, t^{4} + {y'} t \hspace{2em} y( 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?{y} = -4 \, t^{4} + 2 \, t^{3}" alt="{y} = -4 \, t^{4} + 2 \, t^{3}" title="{y} = -4 \, t^{4} + 2 \, t^{3}" data-latex="{y} = -4 \, t^{4} + 2 \, t^{3}"/></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?%7By%7D%20=%20-4%20%5C,%20t%5E%7B4%7D%20+%202%20%5C,%20t%5E%7B3%7D" alt="{y} = -4 \, t^{4} + 2 \, t^{3}" title="{y} = -4 \, t^{4} + 2 \, t^{3}" data-latex="{y} = -4 \, t^{4} + 2 \, t^{3}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-4576" title="F3 | Techniques for linear IVPs | ver. 4576"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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?12 \, t + 2 \, {y} = -t {y'} \hspace{2em} y( 1 )= -6" alt="12 \, t + 2 \, {y} = -t {y'} \hspace{2em} y( 1 )= -6" title="12 \, t + 2 \, {y} = -t {y'} \hspace{2em} y( 1 )= -6" data-latex="12 \, t + 2 \, {y} = -t {y'} \hspace{2em} y( 1 )= -6"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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?12%20%5C,%20t%20+%202%20%5C,%20%7By%7D%20=%20-t%20%7By'%7D%20%5Chspace%7B2em%7D%20y(%201%20)=%20-6" alt="12 \, t + 2 \, {y} = -t {y'} \hspace{2em} y( 1 )= -6" title="12 \, t + 2 \, {y} = -t {y'} \hspace{2em} y( 1 )= -6" data-latex="12 \, t + 2 \, {y} = -t {y'} \hspace{2em} y( 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?{y} = -4 \, t - \frac{2}{t^{2}}" alt="{y} = -4 \, t - \frac{2}{t^{2}}" title="{y} = -4 \, t - \frac{2}{t^{2}}" data-latex="{y} = -4 \, t - \frac{2}{t^{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?%7By%7D%20=%20-4%20%5C,%20t%20-%20%5Cfrac%7B2%7D%7Bt%5E%7B2%7D%7D" alt="{y} = -4 \, t - \frac{2}{t^{2}}" title="{y} = -4 \, t - \frac{2}{t^{2}}" data-latex="{y} = -4 \, t - \frac{2}{t^{2}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-1184" title="F3 | Techniques for linear IVPs | ver. 1184"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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'} t - 3 \, {y} - 8 \, t \hspace{2em} y( -1 )= 6" alt="0 = {y'} t - 3 \, {y} - 8 \, t \hspace{2em} y( -1 )= 6" title="0 = {y'} t - 3 \, {y} - 8 \, t \hspace{2em} y( -1 )= 6" data-latex="0 = {y'} t - 3 \, {y} - 8 \, t \hspace{2em} y( -1 )= 6"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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%20t%20-%203%20%5C,%20%7By%7D%20-%208%20%5C,%20t%20%5Chspace%7B2em%7D%20y(%20-1%20)=%206" alt="0 = {y'} t - 3 \, {y} - 8 \, t \hspace{2em} y( -1 )= 6" title="0 = {y'} t - 3 \, {y} - 8 \, t \hspace{2em} y( -1 )= 6" data-latex="0 = {y'} t - 3 \, {y} - 8 \, t \hspace{2em} y( -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?{y} = -2 \, t^{3} - 4 \, t" alt="{y} = -2 \, t^{3} - 4 \, t" title="{y} = -2 \, t^{3} - 4 \, t" data-latex="{y} = -2 \, t^{3} - 4 \, t"/></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?%7By%7D%20=%20-2%20%5C,%20t%5E%7B3%7D%20-%204%20%5C,%20t" alt="{y} = -2 \, t^{3} - 4 \, t" title="{y} = -2 \, t^{3} - 4 \, t" data-latex="{y} = -2 \, t^{3} - 4 \, t"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-1099" title="F3 | Techniques for linear IVPs | ver. 1099"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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 - 2 \, {y} + \frac{3}{t} = 0 \hspace{2em} y( 1 )= -1" alt="-{y'} t - 2 \, {y} + \frac{3}{t} = 0 \hspace{2em} y( 1 )= -1" title="-{y'} t - 2 \, {y} + \frac{3}{t} = 0 \hspace{2em} y( 1 )= -1" data-latex="-{y'} t - 2 \, {y} + \frac{3}{t} = 0 \hspace{2em} y( 1 )= -1"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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-%202%20%5C,%20%7By%7D%20+%20%5Cfrac%7B3%7D%7Bt%7D%20=%200%20%5Chspace%7B2em%7D%20y(%201%20)=%20-1" alt="-{y'} t - 2 \, {y} + \frac{3}{t} = 0 \hspace{2em} y( 1 )= -1" title="-{y'} t - 2 \, {y} + \frac{3}{t} = 0 \hspace{2em} y( 1 )= -1" data-latex="-{y'} t - 2 \, {y} + \frac{3}{t} = 0 \hspace{2em} y( 1 )= -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?{y} = \frac{3}{t} - \frac{4}{t^{2}}" alt="{y} = \frac{3}{t} - \frac{4}{t^{2}}" title="{y} = \frac{3}{t} - \frac{4}{t^{2}}" data-latex="{y} = \frac{3}{t} - \frac{4}{t^{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?%7By%7D%20=%20%5Cfrac%7B3%7D%7Bt%7D%20-%20%5Cfrac%7B4%7D%7Bt%5E%7B2%7D%7D" alt="{y} = \frac{3}{t} - \frac{4}{t^{2}}" title="{y} = \frac{3}{t} - \frac{4}{t^{2}}" data-latex="{y} = \frac{3}{t} - \frac{4}{t^{2}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F3-7956" title="F3 | Techniques for linear IVPs | ver. 7956"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F3.</strong></p><p>Find the solution to the given 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?4 \, {y} + \frac{6}{t} = -t {y'} \hspace{2em} y( 1 )= 2" alt="4 \, {y} + \frac{6}{t} = -t {y'} \hspace{2em} y( 1 )= 2" title="4 \, {y} + \frac{6}{t} = -t {y'} \hspace{2em} y( 1 )= 2" data-latex="4 \, {y} + \frac{6}{t} = -t {y'} \hspace{2em} y( 1 )= 2"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F3.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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?4%20%5C,%20%7By%7D%20+%20%5Cfrac%7B6%7D%7Bt%7D%20=%20-t%20%7By'%7D%20%5Chspace%7B2em%7D%20y(%201%20)=%202" alt="4 \, {y} + \frac{6}{t} = -t {y'} \hspace{2em} y( 1 )= 2" title="4 \, {y} + \frac{6}{t} = -t {y'} \hspace{2em} y( 1 )= 2" data-latex="4 \, {y} + \frac{6}{t} = -t {y'} \hspace{2em} y( 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?{y} = -\frac{2}{t} + \frac{4}{t^{4}}" alt="{y} = -\frac{2}{t} + \frac{4}{t^{4}}" title="{y} = -\frac{2}{t} + \frac{4}{t^{4}}" data-latex="{y} = -\frac{2}{t} + \frac{4}{t^{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?%7By%7D%20=%20-%5Cfrac%7B2%7D%7Bt%7D%20+%20%5Cfrac%7B4%7D%7Bt%5E%7B4%7D%7D" alt="{y} = -\frac{2}{t} + \frac{4}{t^{4}}" title="{y} = -\frac{2}{t} + \frac{4}{t^{4}}" data-latex="{y} = -\frac{2}{t} + \frac{4}{t^{4}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

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