F2.qti

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  <objectbank ident="F2">
    <qtimetadata>
      <qtimetadatafield><fieldlabel>bank_title</fieldlabel><fieldentry>Differential Equations -- F2</fieldentry></qtimetadatafield>
    </qtimetadata>
  <item ident="F2-3991" title="F2 | Separation of variables | ver. 3991"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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 = -2 \, {y'} t - 4 \, {y} \hspace{2em} y( 3 )= -\frac{1}{9}" alt="0 = -2 \, {y'} t - 4 \, {y} \hspace{2em} y( 3 )= -\frac{1}{9}" title="0 = -2 \, {y'} t - 4 \, {y} \hspace{2em} y( 3 )= -\frac{1}{9}" data-latex="0 = -2 \, {y'} t - 4 \, {y} \hspace{2em} y( 3 )= -\frac{1}{9}"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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=%20-2%20%5C,%20%7By'%7D%20t%20-%204%20%5C,%20%7By%7D%20%5Chspace%7B2em%7D%20y(%203%20)=%20-%5Cfrac%7B1%7D%7B9%7D" alt="0 = -2 \, {y'} t - 4 \, {y} \hspace{2em} y( 3 )= -\frac{1}{9}" title="0 = -2 \, {y'} t - 4 \, {y} \hspace{2em} y( 3 )= -\frac{1}{9}" data-latex="0 = -2 \, {y'} t - 4 \, {y} \hspace{2em} y( 3 )= -\frac{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} = -\frac{1}{t^{2}}" alt="{y} = -\frac{1}{t^{2}}" title="{y} = -\frac{1}{t^{2}}" data-latex="{y} = -\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%7B1%7D%7Bt%5E%7B2%7D%7D" alt="{y} = -\frac{1}{t^{2}}" title="{y} = -\frac{1}{t^{2}}" data-latex="{y} = -\frac{1}{t^{2}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-7535" title="F2 | Separation of variables | ver. 7535"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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} {\left(4 \, t - 1\right)} + 2 \, {y'} = 0 \hspace{2em} y( 0 )= -2 \, e^{2}" alt="2 \, {y} {\left(4 \, t - 1\right)} + 2 \, {y'} = 0 \hspace{2em} y( 0 )= -2 \, e^{2}" title="2 \, {y} {\left(4 \, t - 1\right)} + 2 \, {y'} = 0 \hspace{2em} y( 0 )= -2 \, e^{2}" data-latex="2 \, {y} {\left(4 \, t - 1\right)} + 2 \, {y'} = 0 \hspace{2em} y( 0 )= -2 \, e^{2}"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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%7B%5Cleft(4%20%5C,%20t%20-%201%5Cright)%7D%20+%202%20%5C,%20%7By'%7D%20=%200%20%5Chspace%7B2em%7D%20y(%200%20)=%20-2%20%5C,%20e%5E%7B2%7D" alt="2 \, {y} {\left(4 \, t - 1\right)} + 2 \, {y'} = 0 \hspace{2em} y( 0 )= -2 \, e^{2}" title="2 \, {y} {\left(4 \, t - 1\right)} + 2 \, {y'} = 0 \hspace{2em} y( 0 )= -2 \, e^{2}" data-latex="2 \, {y} {\left(4 \, t - 1\right)} + 2 \, {y'} = 0 \hspace{2em} y( 0 )= -2 \, e^{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 \, e^{\left(-2 \, t^{2} + t + 2\right)}" alt="{y} = -2 \, e^{\left(-2 \, t^{2} + t + 2\right)}" title="{y} = -2 \, e^{\left(-2 \, t^{2} + t + 2\right)}" data-latex="{y} = -2 \, e^{\left(-2 \, t^{2} + t + 2\right)}"/></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,%20e%5E%7B%5Cleft(-2%20%5C,%20t%5E%7B2%7D%20+%20t%20+%202%5Cright)%7D" alt="{y} = -2 \, e^{\left(-2 \, t^{2} + t + 2\right)}" title="{y} = -2 \, e^{\left(-2 \, t^{2} + t + 2\right)}" data-latex="{y} = -2 \, e^{\left(-2 \, t^{2} + t + 2\right)}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-8763" title="F2 | Separation of variables | ver. 8763"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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} = -\frac{12 \, t}{{y}^{2}} - \frac{3}{{y}^{2}} \hspace{2em} y( 2 )= 3" alt="-3 \, {y'} {y} = -\frac{12 \, t}{{y}^{2}} - \frac{3}{{y}^{2}} \hspace{2em} y( 2 )= 3" title="-3 \, {y'} {y} = -\frac{12 \, t}{{y}^{2}} - \frac{3}{{y}^{2}} \hspace{2em} y( 2 )= 3" data-latex="-3 \, {y'} {y} = -\frac{12 \, t}{{y}^{2}} - \frac{3}{{y}^{2}} \hspace{2em} y( 2 )= 3"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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%7By%7D%20=%20-%5Cfrac%7B12%20%5C,%20t%7D%7B%7By%7D%5E%7B2%7D%7D%20-%20%5Cfrac%7B3%7D%7B%7By%7D%5E%7B2%7D%7D%20%5Chspace%7B2em%7D%20y(%202%20)=%203" alt="-3 \, {y'} {y} = -\frac{12 \, t}{{y}^{2}} - \frac{3}{{y}^{2}} \hspace{2em} y( 2 )= 3" title="-3 \, {y'} {y} = -\frac{12 \, t}{{y}^{2}} - \frac{3}{{y}^{2}} \hspace{2em} y( 2 )= 3" data-latex="-3 \, {y'} {y} = -\frac{12 \, t}{{y}^{2}} - \frac{3}{{y}^{2}} \hspace{2em} y( 2 )= 3"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y} = {\left(2 \, t^{2} + t + 17\right)}^{\frac{1}{3}}" alt="{y} = {\left(2 \, t^{2} + t + 17\right)}^{\frac{1}{3}}" title="{y} = {\left(2 \, t^{2} + t + 17\right)}^{\frac{1}{3}}" data-latex="{y} = {\left(2 \, t^{2} + t + 17\right)}^{\frac{1}{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%7B%5Cleft(2%20%5C,%20t%5E%7B2%7D%20+%20t%20+%2017%5Cright)%7D%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D" alt="{y} = {\left(2 \, t^{2} + t + 17\right)}^{\frac{1}{3}}" title="{y} = {\left(2 \, t^{2} + t + 17\right)}^{\frac{1}{3}}" data-latex="{y} = {\left(2 \, t^{2} + t + 17\right)}^{\frac{1}{3}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-1162" title="F2 | Separation of variables | ver. 1162"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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 = -2 \, {y'} t - 6 \, {y} \hspace{2em} y( -2 )= -\frac{3}{8}" alt="0 = -2 \, {y'} t - 6 \, {y} \hspace{2em} y( -2 )= -\frac{3}{8}" title="0 = -2 \, {y'} t - 6 \, {y} \hspace{2em} y( -2 )= -\frac{3}{8}" data-latex="0 = -2 \, {y'} t - 6 \, {y} \hspace{2em} y( -2 )= -\frac{3}{8}"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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=%20-2%20%5C,%20%7By'%7D%20t%20-%206%20%5C,%20%7By%7D%20%5Chspace%7B2em%7D%20y(%20-2%20)=%20-%5Cfrac%7B3%7D%7B8%7D" alt="0 = -2 \, {y'} t - 6 \, {y} \hspace{2em} y( -2 )= -\frac{3}{8}" title="0 = -2 \, {y'} t - 6 \, {y} \hspace{2em} y( -2 )= -\frac{3}{8}" data-latex="0 = -2 \, {y'} t - 6 \, {y} \hspace{2em} y( -2 )= -\frac{3}{8}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y} = \frac{3}{t^{3}}" alt="{y} = \frac{3}{t^{3}}" title="{y} = \frac{3}{t^{3}}" data-latex="{y} = \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%7B3%7D%7Bt%5E%7B3%7D%7D" alt="{y} = \frac{3}{t^{3}}" title="{y} = \frac{3}{t^{3}}" data-latex="{y} = \frac{3}{t^{3}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-8646" title="F2 | Separation of variables | ver. 8646"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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}^{2} {y'} + \frac{12 \, t}{{y}} + \frac{4}{{y}} = 0 \hspace{2em} y( 3 )= 3" alt="-2 \, {y}^{2} {y'} + \frac{12 \, t}{{y}} + \frac{4}{{y}} = 0 \hspace{2em} y( 3 )= 3" title="-2 \, {y}^{2} {y'} + \frac{12 \, t}{{y}} + \frac{4}{{y}} = 0 \hspace{2em} y( 3 )= 3" data-latex="-2 \, {y}^{2} {y'} + \frac{12 \, t}{{y}} + \frac{4}{{y}} = 0 \hspace{2em} y( 3 )= 3"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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%5E%7B2%7D%20%7By'%7D%20+%20%5Cfrac%7B12%20%5C,%20t%7D%7B%7By%7D%7D%20+%20%5Cfrac%7B4%7D%7B%7By%7D%7D%20=%200%20%5Chspace%7B2em%7D%20y(%203%20)=%203" alt="-2 \, {y}^{2} {y'} + \frac{12 \, t}{{y}} + \frac{4}{{y}} = 0 \hspace{2em} y( 3 )= 3" title="-2 \, {y}^{2} {y'} + \frac{12 \, t}{{y}} + \frac{4}{{y}} = 0 \hspace{2em} y( 3 )= 3" data-latex="-2 \, {y}^{2} {y'} + \frac{12 \, t}{{y}} + \frac{4}{{y}} = 0 \hspace{2em} y( 3 )= 3"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y} = {\left(3 \, t^{2} + 2 \, t - 6\right)}^{\frac{1}{3}}" alt="{y} = {\left(3 \, t^{2} + 2 \, t - 6\right)}^{\frac{1}{3}}" title="{y} = {\left(3 \, t^{2} + 2 \, t - 6\right)}^{\frac{1}{3}}" data-latex="{y} = {\left(3 \, t^{2} + 2 \, t - 6\right)}^{\frac{1}{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%7B%5Cleft(3%20%5C,%20t%5E%7B2%7D%20+%202%20%5C,%20t%20-%206%5Cright)%7D%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D" alt="{y} = {\left(3 \, t^{2} + 2 \, t - 6\right)}^{\frac{1}{3}}" title="{y} = {\left(3 \, t^{2} + 2 \, t - 6\right)}^{\frac{1}{3}}" data-latex="{y} = {\left(3 \, t^{2} + 2 \, t - 6\right)}^{\frac{1}{3}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-8863" title="F2 | Separation of variables | ver. 8863"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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 = 2 \, {y'} t - 6 \, {y} \hspace{2em} y( 4 )= -256" alt="0 = 2 \, {y'} t - 6 \, {y} \hspace{2em} y( 4 )= -256" title="0 = 2 \, {y'} t - 6 \, {y} \hspace{2em} y( 4 )= -256" data-latex="0 = 2 \, {y'} t - 6 \, {y} \hspace{2em} y( 4 )= -256"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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=%202%20%5C,%20%7By'%7D%20t%20-%206%20%5C,%20%7By%7D%20%5Chspace%7B2em%7D%20y(%204%20)=%20-256" alt="0 = 2 \, {y'} t - 6 \, {y} \hspace{2em} y( 4 )= -256" title="0 = 2 \, {y'} t - 6 \, {y} \hspace{2em} y( 4 )= -256" data-latex="0 = 2 \, {y'} t - 6 \, {y} \hspace{2em} y( 4 )= -256"&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}" alt="{y} = -4 \, t^{3}" title="{y} = -4 \, t^{3}" data-latex="{y} = -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=%20-4%20%5C,%20t%5E%7B3%7D" alt="{y} = -4 \, t^{3}" title="{y} = -4 \, t^{3}" data-latex="{y} = -4 \, t^{3}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-8319" title="F2 | Separation of variables | ver. 8319"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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} = 2 \, t {y'} \hspace{2em} y( -2 )= \frac{1}{2}" alt="-4 \, {y} = 2 \, t {y'} \hspace{2em} y( -2 )= \frac{1}{2}" title="-4 \, {y} = 2 \, t {y'} \hspace{2em} y( -2 )= \frac{1}{2}" data-latex="-4 \, {y} = 2 \, t {y'} \hspace{2em} y( -2 )= \frac{1}{2}"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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=%202%20%5C,%20t%20%7By'%7D%20%5Chspace%7B2em%7D%20y(%20-2%20)=%20%5Cfrac%7B1%7D%7B2%7D" alt="-4 \, {y} = 2 \, t {y'} \hspace{2em} y( -2 )= \frac{1}{2}" title="-4 \, {y} = 2 \, t {y'} \hspace{2em} y( -2 )= \frac{1}{2}" data-latex="-4 \, {y} = 2 \, t {y'} \hspace{2em} y( -2 )= \frac{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^{2}}" alt="{y} = \frac{2}{t^{2}}" title="{y} = \frac{2}{t^{2}}" data-latex="{y} = \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%5Cfrac%7B2%7D%7Bt%5E%7B2%7D%7D" alt="{y} = \frac{2}{t^{2}}" title="{y} = \frac{2}{t^{2}}" data-latex="{y} = \frac{2}{t^{2}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-6504" title="F2 | Separation of variables | ver. 6504"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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{18 \, t}{{y}} = -3 \, {y} {y'} + \frac{6}{{y}} \hspace{2em} y( 2 )= 2" alt="-\frac{18 \, t}{{y}} = -3 \, {y} {y'} + \frac{6}{{y}} \hspace{2em} y( 2 )= 2" title="-\frac{18 \, t}{{y}} = -3 \, {y} {y'} + \frac{6}{{y}} \hspace{2em} y( 2 )= 2" data-latex="-\frac{18 \, t}{{y}} = -3 \, {y} {y'} + \frac{6}{{y}} \hspace{2em} y( 2 )= 2"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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%7B18%20%5C,%20t%7D%7B%7By%7D%7D%20=%20-3%20%5C,%20%7By%7D%20%7By'%7D%20+%20%5Cfrac%7B6%7D%7B%7By%7D%7D%20%5Chspace%7B2em%7D%20y(%202%20)=%202" alt="-\frac{18 \, t}{{y}} = -3 \, {y} {y'} + \frac{6}{{y}} \hspace{2em} y( 2 )= 2" title="-\frac{18 \, t}{{y}} = -3 \, {y} {y'} + \frac{6}{{y}} \hspace{2em} y( 2 )= 2" data-latex="-\frac{18 \, t}{{y}} = -3 \, {y} {y'} + \frac{6}{{y}} \hspace{2em} y( 2 )= 2"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y} = \sqrt{3 \, t^{2} + 2 \, t - 12}" alt="{y} = \sqrt{3 \, t^{2} + 2 \, t - 12}" title="{y} = \sqrt{3 \, t^{2} + 2 \, t - 12}" data-latex="{y} = \sqrt{3 \, t^{2} + 2 \, t - 12}"/></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%5Csqrt%7B3%20%5C,%20t%5E%7B2%7D%20+%202%20%5C,%20t%20-%2012%7D" alt="{y} = \sqrt{3 \, t^{2} + 2 \, t - 12}" title="{y} = \sqrt{3 \, t^{2} + 2 \, t - 12}" data-latex="{y} = \sqrt{3 \, t^{2} + 2 \, t - 12}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-1080" title="F2 | Separation of variables | ver. 1080"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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'} t = -9 \, {y} \hspace{2em} y( 2 )= -\frac{1}{8}" alt="3 \, {y'} t = -9 \, {y} \hspace{2em} y( 2 )= -\frac{1}{8}" title="3 \, {y'} t = -9 \, {y} \hspace{2em} y( 2 )= -\frac{1}{8}" data-latex="3 \, {y'} t = -9 \, {y} \hspace{2em} y( 2 )= -\frac{1}{8}"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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%20t%20=%20-9%20%5C,%20%7By%7D%20%5Chspace%7B2em%7D%20y(%202%20)=%20-%5Cfrac%7B1%7D%7B8%7D" alt="3 \, {y'} t = -9 \, {y} \hspace{2em} y( 2 )= -\frac{1}{8}" title="3 \, {y'} t = -9 \, {y} \hspace{2em} y( 2 )= -\frac{1}{8}" data-latex="3 \, {y'} t = -9 \, {y} \hspace{2em} y( 2 )= -\frac{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{1}{t^{3}}" alt="{y} = -\frac{1}{t^{3}}" title="{y} = -\frac{1}{t^{3}}" data-latex="{y} = -\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%7B3%7D%7D" alt="{y} = -\frac{1}{t^{3}}" title="{y} = -\frac{1}{t^{3}}" data-latex="{y} = -\frac{1}{t^{3}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-8726" title="F2 | Separation of variables | ver. 8726"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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 = -2 \, {y'} t - 4 \, {y} \hspace{2em} y( 2 )= -1" alt="0 = -2 \, {y'} t - 4 \, {y} \hspace{2em} y( 2 )= -1" title="0 = -2 \, {y'} t - 4 \, {y} \hspace{2em} y( 2 )= -1" data-latex="0 = -2 \, {y'} t - 4 \, {y} \hspace{2em} y( 2 )= -1"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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=%20-2%20%5C,%20%7By'%7D%20t%20-%204%20%5C,%20%7By%7D%20%5Chspace%7B2em%7D%20y(%202%20)=%20-1" alt="0 = -2 \, {y'} t - 4 \, {y} \hspace{2em} y( 2 )= -1" title="0 = -2 \, {y'} t - 4 \, {y} \hspace{2em} y( 2 )= -1" data-latex="0 = -2 \, {y'} t - 4 \, {y} \hspace{2em} y( 2 )= -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}}" alt="{y} = -\frac{4}{t^{2}}" title="{y} = -\frac{4}{t^{2}}" data-latex="{y} = -\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%7B4%7D%7Bt%5E%7B2%7D%7D" alt="{y} = -\frac{4}{t^{2}}" title="{y} = -\frac{4}{t^{2}}" data-latex="{y} = -\frac{4}{t^{2}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-2974" title="F2 | Separation of variables | ver. 2974"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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 \, {y} \sin\left(t\right) = 3 \, {y'} \hspace{2em} y( 0 )= -e^{\left(-2\right)}" alt="6 \, {y} \sin\left(t\right) = 3 \, {y'} \hspace{2em} y( 0 )= -e^{\left(-2\right)}" title="6 \, {y} \sin\left(t\right) = 3 \, {y'} \hspace{2em} y( 0 )= -e^{\left(-2\right)}" data-latex="6 \, {y} \sin\left(t\right) = 3 \, {y'} \hspace{2em} y( 0 )= -e^{\left(-2\right)}"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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,%20%7By%7D%20%5Csin%5Cleft(t%5Cright)%20=%203%20%5C,%20%7By'%7D%20%5Chspace%7B2em%7D%20y(%200%20)=%20-e%5E%7B%5Cleft(-2%5Cright)%7D" alt="6 \, {y} \sin\left(t\right) = 3 \, {y'} \hspace{2em} y( 0 )= -e^{\left(-2\right)}" title="6 \, {y} \sin\left(t\right) = 3 \, {y'} \hspace{2em} y( 0 )= -e^{\left(-2\right)}" data-latex="6 \, {y} \sin\left(t\right) = 3 \, {y'} \hspace{2em} y( 0 )= -e^{\left(-2\right)}"&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} = -e^{\left(-2 \, \cos\left(t\right)\right)}" alt="{y} = -e^{\left(-2 \, \cos\left(t\right)\right)}" title="{y} = -e^{\left(-2 \, \cos\left(t\right)\right)}" data-latex="{y} = -e^{\left(-2 \, \cos\left(t\right)\right)}"/></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-e%5E%7B%5Cleft(-2%20%5C,%20%5Ccos%5Cleft(t%5Cright)%5Cright)%7D" alt="{y} = -e^{\left(-2 \, \cos\left(t\right)\right)}" title="{y} = -e^{\left(-2 \, \cos\left(t\right)\right)}" data-latex="{y} = -e^{\left(-2 \, \cos\left(t\right)\right)}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-1846" title="F2 | Separation of variables | ver. 1846"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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}^{2} {y'} = -\frac{4 \, t}{{y}} - \frac{4}{{y}} \hspace{2em} y( 3 )= 3" alt="-2 \, {y}^{2} {y'} = -\frac{4 \, t}{{y}} - \frac{4}{{y}} \hspace{2em} y( 3 )= 3" title="-2 \, {y}^{2} {y'} = -\frac{4 \, t}{{y}} - \frac{4}{{y}} \hspace{2em} y( 3 )= 3" data-latex="-2 \, {y}^{2} {y'} = -\frac{4 \, t}{{y}} - \frac{4}{{y}} \hspace{2em} y( 3 )= 3"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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%5E%7B2%7D%20%7By'%7D%20=%20-%5Cfrac%7B4%20%5C,%20t%7D%7B%7By%7D%7D%20-%20%5Cfrac%7B4%7D%7B%7By%7D%7D%20%5Chspace%7B2em%7D%20y(%203%20)=%203" alt="-2 \, {y}^{2} {y'} = -\frac{4 \, t}{{y}} - \frac{4}{{y}} \hspace{2em} y( 3 )= 3" title="-2 \, {y}^{2} {y'} = -\frac{4 \, t}{{y}} - \frac{4}{{y}} \hspace{2em} y( 3 )= 3" data-latex="-2 \, {y}^{2} {y'} = -\frac{4 \, t}{{y}} - \frac{4}{{y}} \hspace{2em} y( 3 )= 3"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y} = {\left(t^{2} + 2 \, t + 12\right)}^{\frac{1}{3}}" alt="{y} = {\left(t^{2} + 2 \, t + 12\right)}^{\frac{1}{3}}" title="{y} = {\left(t^{2} + 2 \, t + 12\right)}^{\frac{1}{3}}" data-latex="{y} = {\left(t^{2} + 2 \, t + 12\right)}^{\frac{1}{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%7B%5Cleft(t%5E%7B2%7D%20+%202%20%5C,%20t%20+%2012%5Cright)%7D%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D" alt="{y} = {\left(t^{2} + 2 \, t + 12\right)}^{\frac{1}{3}}" title="{y} = {\left(t^{2} + 2 \, t + 12\right)}^{\frac{1}{3}}" data-latex="{y} = {\left(t^{2} + 2 \, t + 12\right)}^{\frac{1}{3}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-1776" title="F2 | Separation of variables | ver. 1776"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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 = -2 \, {y} \cos\left(t\right) - 2 \, {y'} \hspace{2em} y( 0 )= 3" alt="0 = -2 \, {y} \cos\left(t\right) - 2 \, {y'} \hspace{2em} y( 0 )= 3" title="0 = -2 \, {y} \cos\left(t\right) - 2 \, {y'} \hspace{2em} y( 0 )= 3" data-latex="0 = -2 \, {y} \cos\left(t\right) - 2 \, {y'} \hspace{2em} y( 0 )= 3"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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=%20-2%20%5C,%20%7By%7D%20%5Ccos%5Cleft(t%5Cright)%20-%202%20%5C,%20%7By'%7D%20%5Chspace%7B2em%7D%20y(%200%20)=%203" alt="0 = -2 \, {y} \cos\left(t\right) - 2 \, {y'} \hspace{2em} y( 0 )= 3" title="0 = -2 \, {y} \cos\left(t\right) - 2 \, {y'} \hspace{2em} y( 0 )= 3" data-latex="0 = -2 \, {y} \cos\left(t\right) - 2 \, {y'} \hspace{2em} y( 0 )= 3"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y} = 3 \, e^{\left(-\sin\left(t\right)\right)}" alt="{y} = 3 \, e^{\left(-\sin\left(t\right)\right)}" title="{y} = 3 \, e^{\left(-\sin\left(t\right)\right)}" data-latex="{y} = 3 \, e^{\left(-\sin\left(t\right)\right)}"/></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,%20e%5E%7B%5Cleft(-%5Csin%5Cleft(t%5Cright)%5Cright)%7D" alt="{y} = 3 \, e^{\left(-\sin\left(t\right)\right)}" title="{y} = 3 \, e^{\left(-\sin\left(t\right)\right)}" data-latex="{y} = 3 \, e^{\left(-\sin\left(t\right)\right)}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-3192" title="F2 | Separation of variables | ver. 3192"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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'} = \frac{6 \, t}{{y}} + \frac{6}{{y}} \hspace{2em} y( 2 )= 3" alt="3 \, {y} {y'} = \frac{6 \, t}{{y}} + \frac{6}{{y}} \hspace{2em} y( 2 )= 3" title="3 \, {y} {y'} = \frac{6 \, t}{{y}} + \frac{6}{{y}} \hspace{2em} y( 2 )= 3" data-latex="3 \, {y} {y'} = \frac{6 \, t}{{y}} + \frac{6}{{y}} \hspace{2em} y( 2 )= 3"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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%7By'%7D%20=%20%5Cfrac%7B6%20%5C,%20t%7D%7B%7By%7D%7D%20+%20%5Cfrac%7B6%7D%7B%7By%7D%7D%20%5Chspace%7B2em%7D%20y(%202%20)=%203" alt="3 \, {y} {y'} = \frac{6 \, t}{{y}} + \frac{6}{{y}} \hspace{2em} y( 2 )= 3" title="3 \, {y} {y'} = \frac{6 \, t}{{y}} + \frac{6}{{y}} \hspace{2em} y( 2 )= 3" data-latex="3 \, {y} {y'} = \frac{6 \, t}{{y}} + \frac{6}{{y}} \hspace{2em} y( 2 )= 3"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y} = \sqrt{t^{2} + 2 \, t + 1}" alt="{y} = \sqrt{t^{2} + 2 \, t + 1}" title="{y} = \sqrt{t^{2} + 2 \, t + 1}" data-latex="{y} = \sqrt{t^{2} + 2 \, t + 1}"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%7By%7D%20=%20%5Csqrt%7Bt%5E%7B2%7D%20+%202%20%5C,%20t%20+%201%7D" alt="{y} = \sqrt{t^{2} + 2 \, t + 1}" title="{y} = \sqrt{t^{2} + 2 \, t + 1}" data-latex="{y} = \sqrt{t^{2} + 2 \, t + 1}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-8674" title="F2 | Separation of variables | ver. 8674"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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 = 6 \, {y} \hspace{2em} y( -1 )= 4" alt="-2 \, {y'} t = 6 \, {y} \hspace{2em} y( -1 )= 4" title="-2 \, {y'} t = 6 \, {y} \hspace{2em} y( -1 )= 4" data-latex="-2 \, {y'} t = 6 \, {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;F2.&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%20t%20=%206%20%5C,%20%7By%7D%20%5Chspace%7B2em%7D%20y(%20-1%20)=%204" alt="-2 \, {y'} t = 6 \, {y} \hspace{2em} y( -1 )= 4" title="-2 \, {y'} t = 6 \, {y} \hspace{2em} y( -1 )= 4" data-latex="-2 \, {y'} t = 6 \, {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{4}{t^{3}}" alt="{y} = -\frac{4}{t^{3}}" title="{y} = -\frac{4}{t^{3}}" data-latex="{y} = -\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-%5Cfrac%7B4%7D%7Bt%5E%7B3%7D%7D" alt="{y} = -\frac{4}{t^{3}}" title="{y} = -\frac{4}{t^{3}}" data-latex="{y} = -\frac{4}{t^{3}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-6274" title="F2 | Separation of variables | ver. 6274"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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{4 \, t}{{y}^{2}} = 2 \, {y} {y'} - \frac{4}{{y}^{2}} \hspace{2em} y( -2 )= 2" alt="\frac{4 \, t}{{y}^{2}} = 2 \, {y} {y'} - \frac{4}{{y}^{2}} \hspace{2em} y( -2 )= 2" title="\frac{4 \, t}{{y}^{2}} = 2 \, {y} {y'} - \frac{4}{{y}^{2}} \hspace{2em} y( -2 )= 2" data-latex="\frac{4 \, t}{{y}^{2}} = 2 \, {y} {y'} - \frac{4}{{y}^{2}} \hspace{2em} y( -2 )= 2"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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%7B4%20%5C,%20t%7D%7B%7By%7D%5E%7B2%7D%7D%20=%202%20%5C,%20%7By%7D%20%7By'%7D%20-%20%5Cfrac%7B4%7D%7B%7By%7D%5E%7B2%7D%7D%20%5Chspace%7B2em%7D%20y(%20-2%20)=%202" alt="\frac{4 \, t}{{y}^{2}} = 2 \, {y} {y'} - \frac{4}{{y}^{2}} \hspace{2em} y( -2 )= 2" title="\frac{4 \, t}{{y}^{2}} = 2 \, {y} {y'} - \frac{4}{{y}^{2}} \hspace{2em} y( -2 )= 2" data-latex="\frac{4 \, t}{{y}^{2}} = 2 \, {y} {y'} - \frac{4}{{y}^{2}} \hspace{2em} y( -2 )= 2"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y} = {\left(t^{2} + 2 \, t + 8\right)}^{\frac{1}{3}}" alt="{y} = {\left(t^{2} + 2 \, t + 8\right)}^{\frac{1}{3}}" title="{y} = {\left(t^{2} + 2 \, t + 8\right)}^{\frac{1}{3}}" data-latex="{y} = {\left(t^{2} + 2 \, t + 8\right)}^{\frac{1}{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%7B%5Cleft(t%5E%7B2%7D%20+%202%20%5C,%20t%20+%208%5Cright)%7D%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D" alt="{y} = {\left(t^{2} + 2 \, t + 8\right)}^{\frac{1}{3}}" title="{y} = {\left(t^{2} + 2 \, t + 8\right)}^{\frac{1}{3}}" data-latex="{y} = {\left(t^{2} + 2 \, t + 8\right)}^{\frac{1}{3}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-0709" title="F2 | Separation of variables | ver. 0709"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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} \sin\left(t\right) = -2 \, {y'} \hspace{2em} y( 0 )= -2 \, e" alt="2 \, {y} \sin\left(t\right) = -2 \, {y'} \hspace{2em} y( 0 )= -2 \, e" title="2 \, {y} \sin\left(t\right) = -2 \, {y'} \hspace{2em} y( 0 )= -2 \, e" data-latex="2 \, {y} \sin\left(t\right) = -2 \, {y'} \hspace{2em} y( 0 )= -2 \, e"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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%5Csin%5Cleft(t%5Cright)%20=%20-2%20%5C,%20%7By'%7D%20%5Chspace%7B2em%7D%20y(%200%20)=%20-2%20%5C,%20e" alt="2 \, {y} \sin\left(t\right) = -2 \, {y'} \hspace{2em} y( 0 )= -2 \, e" title="2 \, {y} \sin\left(t\right) = -2 \, {y'} \hspace{2em} y( 0 )= -2 \, e" data-latex="2 \, {y} \sin\left(t\right) = -2 \, {y'} \hspace{2em} y( 0 )= -2 \, e"&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 \, e^{\cos\left(t\right)}" alt="{y} = -2 \, e^{\cos\left(t\right)}" title="{y} = -2 \, e^{\cos\left(t\right)}" data-latex="{y} = -2 \, e^{\cos\left(t\right)}"/></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,%20e%5E%7B%5Ccos%5Cleft(t%5Cright)%7D" alt="{y} = -2 \, e^{\cos\left(t\right)}" title="{y} = -2 \, e^{\cos\left(t\right)}" data-latex="{y} = -2 \, e^{\cos\left(t\right)}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-0829" title="F2 | Separation of variables | ver. 0829"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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 = -3 \, {y} {\left(6 \, t - 1\right)} - 3 \, {y'} \hspace{2em} y( 0 )= -3 \, e^{3}" alt="0 = -3 \, {y} {\left(6 \, t - 1\right)} - 3 \, {y'} \hspace{2em} y( 0 )= -3 \, e^{3}" title="0 = -3 \, {y} {\left(6 \, t - 1\right)} - 3 \, {y'} \hspace{2em} y( 0 )= -3 \, e^{3}" data-latex="0 = -3 \, {y} {\left(6 \, t - 1\right)} - 3 \, {y'} \hspace{2em} y( 0 )= -3 \, e^{3}"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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=%20-3%20%5C,%20%7By%7D%20%7B%5Cleft(6%20%5C,%20t%20-%201%5Cright)%7D%20-%203%20%5C,%20%7By'%7D%20%5Chspace%7B2em%7D%20y(%200%20)=%20-3%20%5C,%20e%5E%7B3%7D" alt="0 = -3 \, {y} {\left(6 \, t - 1\right)} - 3 \, {y'} \hspace{2em} y( 0 )= -3 \, e^{3}" title="0 = -3 \, {y} {\left(6 \, t - 1\right)} - 3 \, {y'} \hspace{2em} y( 0 )= -3 \, e^{3}" data-latex="0 = -3 \, {y} {\left(6 \, t - 1\right)} - 3 \, {y'} \hspace{2em} y( 0 )= -3 \, e^{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} = -3 \, e^{\left(-3 \, t^{2} + t + 3\right)}" alt="{y} = -3 \, e^{\left(-3 \, t^{2} + t + 3\right)}" title="{y} = -3 \, e^{\left(-3 \, t^{2} + t + 3\right)}" data-latex="{y} = -3 \, e^{\left(-3 \, t^{2} + t + 3\right)}"/></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,%20e%5E%7B%5Cleft(-3%20%5C,%20t%5E%7B2%7D%20+%20t%20+%203%5Cright)%7D" alt="{y} = -3 \, e^{\left(-3 \, t^{2} + t + 3\right)}" title="{y} = -3 \, e^{\left(-3 \, t^{2} + t + 3\right)}" data-latex="{y} = -3 \, e^{\left(-3 \, t^{2} + t + 3\right)}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-6873" title="F2 | Separation of variables | ver. 6873"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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'} = -2 \, {y} \sin\left(t\right) \hspace{2em} y( 0 )= -e^{\left(-1\right)}" alt="-2 \, {y'} = -2 \, {y} \sin\left(t\right) \hspace{2em} y( 0 )= -e^{\left(-1\right)}" title="-2 \, {y'} = -2 \, {y} \sin\left(t\right) \hspace{2em} y( 0 )= -e^{\left(-1\right)}" data-latex="-2 \, {y'} = -2 \, {y} \sin\left(t\right) \hspace{2em} y( 0 )= -e^{\left(-1\right)}"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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=%20-2%20%5C,%20%7By%7D%20%5Csin%5Cleft(t%5Cright)%20%5Chspace%7B2em%7D%20y(%200%20)=%20-e%5E%7B%5Cleft(-1%5Cright)%7D" alt="-2 \, {y'} = -2 \, {y} \sin\left(t\right) \hspace{2em} y( 0 )= -e^{\left(-1\right)}" title="-2 \, {y'} = -2 \, {y} \sin\left(t\right) \hspace{2em} y( 0 )= -e^{\left(-1\right)}" data-latex="-2 \, {y'} = -2 \, {y} \sin\left(t\right) \hspace{2em} y( 0 )= -e^{\left(-1\right)}"&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} = -e^{\left(-\cos\left(t\right)\right)}" alt="{y} = -e^{\left(-\cos\left(t\right)\right)}" title="{y} = -e^{\left(-\cos\left(t\right)\right)}" data-latex="{y} = -e^{\left(-\cos\left(t\right)\right)}"/></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-e%5E%7B%5Cleft(-%5Ccos%5Cleft(t%5Cright)%5Cright)%7D" alt="{y} = -e^{\left(-\cos\left(t\right)\right)}" title="{y} = -e^{\left(-\cos\left(t\right)\right)}" data-latex="{y} = -e^{\left(-\cos\left(t\right)\right)}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-6909" title="F2 | Separation of variables | ver. 6909"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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 = -2 \, {y'} t - 4 \, {y} \hspace{2em} y( 3 )= \frac{1}{3}" alt="0 = -2 \, {y'} t - 4 \, {y} \hspace{2em} y( 3 )= \frac{1}{3}" title="0 = -2 \, {y'} t - 4 \, {y} \hspace{2em} y( 3 )= \frac{1}{3}" data-latex="0 = -2 \, {y'} t - 4 \, {y} \hspace{2em} y( 3 )= \frac{1}{3}"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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=%20-2%20%5C,%20%7By'%7D%20t%20-%204%20%5C,%20%7By%7D%20%5Chspace%7B2em%7D%20y(%203%20)=%20%5Cfrac%7B1%7D%7B3%7D" alt="0 = -2 \, {y'} t - 4 \, {y} \hspace{2em} y( 3 )= \frac{1}{3}" title="0 = -2 \, {y'} t - 4 \, {y} \hspace{2em} y( 3 )= \frac{1}{3}" data-latex="0 = -2 \, {y'} t - 4 \, {y} \hspace{2em} y( 3 )= \frac{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{3}{t^{2}}" alt="{y} = \frac{3}{t^{2}}" title="{y} = \frac{3}{t^{2}}" data-latex="{y} = \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%5Cfrac%7B3%7D%7Bt%5E%7B2%7D%7D" alt="{y} = \frac{3}{t^{2}}" title="{y} = \frac{3}{t^{2}}" data-latex="{y} = \frac{3}{t^{2}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-7516" title="F2 | Separation of variables | ver. 7516"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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?-9 \, {y} = -3 \, {y'} t \hspace{2em} y( -1 )= -4" alt="-9 \, {y} = -3 \, {y'} t \hspace{2em} y( -1 )= -4" title="-9 \, {y} = -3 \, {y'} t \hspace{2em} y( -1 )= -4" data-latex="-9 \, {y} = -3 \, {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;F2.&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?-9%20%5C,%20%7By%7D%20=%20-3%20%5C,%20%7By'%7D%20t%20%5Chspace%7B2em%7D%20y(%20-1%20)=%20-4" alt="-9 \, {y} = -3 \, {y'} t \hspace{2em} y( -1 )= -4" title="-9 \, {y} = -3 \, {y'} t \hspace{2em} y( -1 )= -4" data-latex="-9 \, {y} = -3 \, {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} = 4 \, t^{3}" alt="{y} = 4 \, t^{3}" title="{y} = 4 \, t^{3}" data-latex="{y} = 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=%204%20%5C,%20t%5E%7B3%7D" alt="{y} = 4 \, t^{3}" title="{y} = 4 \, t^{3}" data-latex="{y} = 4 \, t^{3}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-0600" title="F2 | Separation of variables | ver. 0600"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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 = 2 \, {y'} t - 4 \, {y} \hspace{2em} y( 2 )= 12" alt="0 = 2 \, {y'} t - 4 \, {y} \hspace{2em} y( 2 )= 12" title="0 = 2 \, {y'} t - 4 \, {y} \hspace{2em} y( 2 )= 12" data-latex="0 = 2 \, {y'} t - 4 \, {y} \hspace{2em} y( 2 )= 12"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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=%202%20%5C,%20%7By'%7D%20t%20-%204%20%5C,%20%7By%7D%20%5Chspace%7B2em%7D%20y(%202%20)=%2012" alt="0 = 2 \, {y'} t - 4 \, {y} \hspace{2em} y( 2 )= 12" title="0 = 2 \, {y'} t - 4 \, {y} \hspace{2em} y( 2 )= 12" data-latex="0 = 2 \, {y'} t - 4 \, {y} \hspace{2em} y( 2 )= 12"&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}" alt="{y} = 3 \, t^{2}" title="{y} = 3 \, t^{2}" data-latex="{y} = 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=%203%20%5C,%20t%5E%7B2%7D" alt="{y} = 3 \, t^{2}" title="{y} = 3 \, t^{2}" data-latex="{y} = 3 \, t^{2}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-1416" title="F2 | Separation of variables | ver. 1416"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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'} t - 9 \, {y} = 0 \hspace{2em} y( -4 )= -\frac{3}{64}" alt="-3 \, {y'} t - 9 \, {y} = 0 \hspace{2em} y( -4 )= -\frac{3}{64}" title="-3 \, {y'} t - 9 \, {y} = 0 \hspace{2em} y( -4 )= -\frac{3}{64}" data-latex="-3 \, {y'} t - 9 \, {y} = 0 \hspace{2em} y( -4 )= -\frac{3}{64}"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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%20t%20-%209%20%5C,%20%7By%7D%20=%200%20%5Chspace%7B2em%7D%20y(%20-4%20)=%20-%5Cfrac%7B3%7D%7B64%7D" alt="-3 \, {y'} t - 9 \, {y} = 0 \hspace{2em} y( -4 )= -\frac{3}{64}" title="-3 \, {y'} t - 9 \, {y} = 0 \hspace{2em} y( -4 )= -\frac{3}{64}" data-latex="-3 \, {y'} t - 9 \, {y} = 0 \hspace{2em} y( -4 )= -\frac{3}{64}"&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}}" alt="{y} = \frac{3}{t^{3}}" title="{y} = \frac{3}{t^{3}}" data-latex="{y} = \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%7B3%7D%7Bt%5E%7B3%7D%7D" alt="{y} = \frac{3}{t^{3}}" title="{y} = \frac{3}{t^{3}}" data-latex="{y} = \frac{3}{t^{3}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-2499" title="F2 | Separation of variables | ver. 2499"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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'} {y} - \frac{2}{{y}^{2}} = \frac{8 \, t}{{y}^{2}} \hspace{2em} y( 3 )= 3" alt="2 \, {y'} {y} - \frac{2}{{y}^{2}} = \frac{8 \, t}{{y}^{2}} \hspace{2em} y( 3 )= 3" title="2 \, {y'} {y} - \frac{2}{{y}^{2}} = \frac{8 \, t}{{y}^{2}} \hspace{2em} y( 3 )= 3" data-latex="2 \, {y'} {y} - \frac{2}{{y}^{2}} = \frac{8 \, t}{{y}^{2}} \hspace{2em} y( 3 )= 3"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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%7By%7D%20-%20%5Cfrac%7B2%7D%7B%7By%7D%5E%7B2%7D%7D%20=%20%5Cfrac%7B8%20%5C,%20t%7D%7B%7By%7D%5E%7B2%7D%7D%20%5Chspace%7B2em%7D%20y(%203%20)=%203" alt="2 \, {y'} {y} - \frac{2}{{y}^{2}} = \frac{8 \, t}{{y}^{2}} \hspace{2em} y( 3 )= 3" title="2 \, {y'} {y} - \frac{2}{{y}^{2}} = \frac{8 \, t}{{y}^{2}} \hspace{2em} y( 3 )= 3" data-latex="2 \, {y'} {y} - \frac{2}{{y}^{2}} = \frac{8 \, t}{{y}^{2}} \hspace{2em} y( 3 )= 3"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y} = {\left(2 \, t^{2} + t + 6\right)}^{\frac{1}{3}}" alt="{y} = {\left(2 \, t^{2} + t + 6\right)}^{\frac{1}{3}}" title="{y} = {\left(2 \, t^{2} + t + 6\right)}^{\frac{1}{3}}" data-latex="{y} = {\left(2 \, t^{2} + t + 6\right)}^{\frac{1}{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%7B%5Cleft(2%20%5C,%20t%5E%7B2%7D%20+%20t%20+%206%5Cright)%7D%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D" alt="{y} = {\left(2 \, t^{2} + t + 6\right)}^{\frac{1}{3}}" title="{y} = {\left(2 \, t^{2} + t + 6\right)}^{\frac{1}{3}}" data-latex="{y} = {\left(2 \, t^{2} + t + 6\right)}^{\frac{1}{3}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-7463" title="F2 | Separation of variables | ver. 7463"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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{4 \, t}{{y}} + \frac{4}{{y}} = 2 \, {y'} {y}^{2} \hspace{2em} y( -2 )= 4" alt="\frac{4 \, t}{{y}} + \frac{4}{{y}} = 2 \, {y'} {y}^{2} \hspace{2em} y( -2 )= 4" title="\frac{4 \, t}{{y}} + \frac{4}{{y}} = 2 \, {y'} {y}^{2} \hspace{2em} y( -2 )= 4" data-latex="\frac{4 \, t}{{y}} + \frac{4}{{y}} = 2 \, {y'} {y}^{2} \hspace{2em} y( -2 )= 4"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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%7B4%20%5C,%20t%7D%7B%7By%7D%7D%20+%20%5Cfrac%7B4%7D%7B%7By%7D%7D%20=%202%20%5C,%20%7By'%7D%20%7By%7D%5E%7B2%7D%20%5Chspace%7B2em%7D%20y(%20-2%20)=%204" alt="\frac{4 \, t}{{y}} + \frac{4}{{y}} = 2 \, {y'} {y}^{2} \hspace{2em} y( -2 )= 4" title="\frac{4 \, t}{{y}} + \frac{4}{{y}} = 2 \, {y'} {y}^{2} \hspace{2em} y( -2 )= 4" data-latex="\frac{4 \, t}{{y}} + \frac{4}{{y}} = 2 \, {y'} {y}^{2} \hspace{2em} y( -2 )= 4"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y} = {\left(t^{2} + 2 \, t + 64\right)}^{\frac{1}{3}}" alt="{y} = {\left(t^{2} + 2 \, t + 64\right)}^{\frac{1}{3}}" title="{y} = {\left(t^{2} + 2 \, t + 64\right)}^{\frac{1}{3}}" data-latex="{y} = {\left(t^{2} + 2 \, t + 64\right)}^{\frac{1}{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%7B%5Cleft(t%5E%7B2%7D%20+%202%20%5C,%20t%20+%2064%5Cright)%7D%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D" alt="{y} = {\left(t^{2} + 2 \, t + 64\right)}^{\frac{1}{3}}" title="{y} = {\left(t^{2} + 2 \, t + 64\right)}^{\frac{1}{3}}" data-latex="{y} = {\left(t^{2} + 2 \, t + 64\right)}^{\frac{1}{3}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-6198" title="F2 | Separation of variables | ver. 6198"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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{4 \, t}{{y}^{2}} = 2 \, {y} {y'} - \frac{2}{{y}^{2}} \hspace{2em} y( 3 )= 4" alt="\frac{4 \, t}{{y}^{2}} = 2 \, {y} {y'} - \frac{2}{{y}^{2}} \hspace{2em} y( 3 )= 4" title="\frac{4 \, t}{{y}^{2}} = 2 \, {y} {y'} - \frac{2}{{y}^{2}} \hspace{2em} y( 3 )= 4" data-latex="\frac{4 \, t}{{y}^{2}} = 2 \, {y} {y'} - \frac{2}{{y}^{2}} \hspace{2em} y( 3 )= 4"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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%7B4%20%5C,%20t%7D%7B%7By%7D%5E%7B2%7D%7D%20=%202%20%5C,%20%7By%7D%20%7By'%7D%20-%20%5Cfrac%7B2%7D%7B%7By%7D%5E%7B2%7D%7D%20%5Chspace%7B2em%7D%20y(%203%20)=%204" alt="\frac{4 \, t}{{y}^{2}} = 2 \, {y} {y'} - \frac{2}{{y}^{2}} \hspace{2em} y( 3 )= 4" title="\frac{4 \, t}{{y}^{2}} = 2 \, {y} {y'} - \frac{2}{{y}^{2}} \hspace{2em} y( 3 )= 4" data-latex="\frac{4 \, t}{{y}^{2}} = 2 \, {y} {y'} - \frac{2}{{y}^{2}} \hspace{2em} y( 3 )= 4"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y} = {\left(t^{2} + t + 52\right)}^{\frac{1}{3}}" alt="{y} = {\left(t^{2} + t + 52\right)}^{\frac{1}{3}}" title="{y} = {\left(t^{2} + t + 52\right)}^{\frac{1}{3}}" data-latex="{y} = {\left(t^{2} + t + 52\right)}^{\frac{1}{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%7B%5Cleft(t%5E%7B2%7D%20+%20t%20+%2052%5Cright)%7D%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D" alt="{y} = {\left(t^{2} + t + 52\right)}^{\frac{1}{3}}" title="{y} = {\left(t^{2} + t + 52\right)}^{\frac{1}{3}}" data-latex="{y} = {\left(t^{2} + t + 52\right)}^{\frac{1}{3}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-6888" title="F2 | Separation of variables | ver. 6888"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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} - \frac{3}{{y}} = \frac{12 \, t}{{y}} \hspace{2em} y( 2 )= 3" alt="3 \, {y'} {y} - \frac{3}{{y}} = \frac{12 \, t}{{y}} \hspace{2em} y( 2 )= 3" title="3 \, {y'} {y} - \frac{3}{{y}} = \frac{12 \, t}{{y}} \hspace{2em} y( 2 )= 3" data-latex="3 \, {y'} {y} - \frac{3}{{y}} = \frac{12 \, t}{{y}} \hspace{2em} y( 2 )= 3"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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%7By%7D%20-%20%5Cfrac%7B3%7D%7B%7By%7D%7D%20=%20%5Cfrac%7B12%20%5C,%20t%7D%7B%7By%7D%7D%20%5Chspace%7B2em%7D%20y(%202%20)=%203" alt="3 \, {y'} {y} - \frac{3}{{y}} = \frac{12 \, t}{{y}} \hspace{2em} y( 2 )= 3" title="3 \, {y'} {y} - \frac{3}{{y}} = \frac{12 \, t}{{y}} \hspace{2em} y( 2 )= 3" data-latex="3 \, {y'} {y} - \frac{3}{{y}} = \frac{12 \, t}{{y}} \hspace{2em} y( 2 )= 3"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y} = \sqrt{2 \, t^{2} + t - 1}" alt="{y} = \sqrt{2 \, t^{2} + t - 1}" title="{y} = \sqrt{2 \, t^{2} + t - 1}" data-latex="{y} = \sqrt{2 \, t^{2} + t - 1}"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%7By%7D%20=%20%5Csqrt%7B2%20%5C,%20t%5E%7B2%7D%20+%20t%20-%201%7D" alt="{y} = \sqrt{2 \, t^{2} + t - 1}" title="{y} = \sqrt{2 \, t^{2} + t - 1}" data-latex="{y} = \sqrt{2 \, t^{2} + t - 1}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-5313" title="F2 | Separation of variables | ver. 5313"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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{18 \, t}{{y}} - \frac{6}{{y}} = -3 \, {y'} {y}^{2} \hspace{2em} y( -2 )= 2" alt="-\frac{18 \, t}{{y}} - \frac{6}{{y}} = -3 \, {y'} {y}^{2} \hspace{2em} y( -2 )= 2" title="-\frac{18 \, t}{{y}} - \frac{6}{{y}} = -3 \, {y'} {y}^{2} \hspace{2em} y( -2 )= 2" data-latex="-\frac{18 \, t}{{y}} - \frac{6}{{y}} = -3 \, {y'} {y}^{2} \hspace{2em} y( -2 )= 2"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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%7B18%20%5C,%20t%7D%7B%7By%7D%7D%20-%20%5Cfrac%7B6%7D%7B%7By%7D%7D%20=%20-3%20%5C,%20%7By'%7D%20%7By%7D%5E%7B2%7D%20%5Chspace%7B2em%7D%20y(%20-2%20)=%202" alt="-\frac{18 \, t}{{y}} - \frac{6}{{y}} = -3 \, {y'} {y}^{2} \hspace{2em} y( -2 )= 2" title="-\frac{18 \, t}{{y}} - \frac{6}{{y}} = -3 \, {y'} {y}^{2} \hspace{2em} y( -2 )= 2" data-latex="-\frac{18 \, t}{{y}} - \frac{6}{{y}} = -3 \, {y'} {y}^{2} \hspace{2em} y( -2 )= 2"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y} = {\left(3 \, t^{2} + 2 \, t\right)}^{\frac{1}{3}}" alt="{y} = {\left(3 \, t^{2} + 2 \, t\right)}^{\frac{1}{3}}" title="{y} = {\left(3 \, t^{2} + 2 \, t\right)}^{\frac{1}{3}}" data-latex="{y} = {\left(3 \, t^{2} + 2 \, t\right)}^{\frac{1}{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%7B%5Cleft(3%20%5C,%20t%5E%7B2%7D%20+%202%20%5C,%20t%5Cright)%7D%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D" alt="{y} = {\left(3 \, t^{2} + 2 \, t\right)}^{\frac{1}{3}}" title="{y} = {\left(3 \, t^{2} + 2 \, t\right)}^{\frac{1}{3}}" data-latex="{y} = {\left(3 \, t^{2} + 2 \, t\right)}^{\frac{1}{3}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-1918" title="F2 | Separation of variables | ver. 1918"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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}^{2} = \frac{18 \, t}{{y}} + \frac{3}{{y}} \hspace{2em} y( -3 )= 3" alt="3 \, {y'} {y}^{2} = \frac{18 \, t}{{y}} + \frac{3}{{y}} \hspace{2em} y( -3 )= 3" title="3 \, {y'} {y}^{2} = \frac{18 \, t}{{y}} + \frac{3}{{y}} \hspace{2em} y( -3 )= 3" data-latex="3 \, {y'} {y}^{2} = \frac{18 \, t}{{y}} + \frac{3}{{y}} \hspace{2em} y( -3 )= 3"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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%7By%7D%5E%7B2%7D%20=%20%5Cfrac%7B18%20%5C,%20t%7D%7B%7By%7D%7D%20+%20%5Cfrac%7B3%7D%7B%7By%7D%7D%20%5Chspace%7B2em%7D%20y(%20-3%20)=%203" alt="3 \, {y'} {y}^{2} = \frac{18 \, t}{{y}} + \frac{3}{{y}} \hspace{2em} y( -3 )= 3" title="3 \, {y'} {y}^{2} = \frac{18 \, t}{{y}} + \frac{3}{{y}} \hspace{2em} y( -3 )= 3" data-latex="3 \, {y'} {y}^{2} = \frac{18 \, t}{{y}} + \frac{3}{{y}} \hspace{2em} y( -3 )= 3"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y} = {\left(3 \, t^{2} + t + 3\right)}^{\frac{1}{3}}" alt="{y} = {\left(3 \, t^{2} + t + 3\right)}^{\frac{1}{3}}" title="{y} = {\left(3 \, t^{2} + t + 3\right)}^{\frac{1}{3}}" data-latex="{y} = {\left(3 \, t^{2} + t + 3\right)}^{\frac{1}{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%7B%5Cleft(3%20%5C,%20t%5E%7B2%7D%20+%20t%20+%203%5Cright)%7D%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D" alt="{y} = {\left(3 \, t^{2} + t + 3\right)}^{\frac{1}{3}}" title="{y} = {\left(3 \, t^{2} + t + 3\right)}^{\frac{1}{3}}" data-latex="{y} = {\left(3 \, t^{2} + t + 3\right)}^{\frac{1}{3}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-3152" title="F2 | Separation of variables | ver. 3152"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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 = -2 \, {y'} t + 4 \, {y} \hspace{2em} y( 3 )= 27" alt="0 = -2 \, {y'} t + 4 \, {y} \hspace{2em} y( 3 )= 27" title="0 = -2 \, {y'} t + 4 \, {y} \hspace{2em} y( 3 )= 27" data-latex="0 = -2 \, {y'} t + 4 \, {y} \hspace{2em} y( 3 )= 27"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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=%20-2%20%5C,%20%7By'%7D%20t%20+%204%20%5C,%20%7By%7D%20%5Chspace%7B2em%7D%20y(%203%20)=%2027" alt="0 = -2 \, {y'} t + 4 \, {y} \hspace{2em} y( 3 )= 27" title="0 = -2 \, {y'} t + 4 \, {y} \hspace{2em} y( 3 )= 27" data-latex="0 = -2 \, {y'} t + 4 \, {y} \hspace{2em} y( 3 )= 27"&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}" alt="{y} = 3 \, t^{2}" title="{y} = 3 \, t^{2}" data-latex="{y} = 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=%203%20%5C,%20t%5E%7B2%7D" alt="{y} = 3 \, t^{2}" title="{y} = 3 \, t^{2}" data-latex="{y} = 3 \, t^{2}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-8562" title="F2 | Separation of variables | ver. 8562"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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 = -2 \, {y} {\left(2 \, t - 3\right)} + 2 \, {y'} \hspace{2em} y( 0 )= 4 \, e^{4}" alt="0 = -2 \, {y} {\left(2 \, t - 3\right)} + 2 \, {y'} \hspace{2em} y( 0 )= 4 \, e^{4}" title="0 = -2 \, {y} {\left(2 \, t - 3\right)} + 2 \, {y'} \hspace{2em} y( 0 )= 4 \, e^{4}" data-latex="0 = -2 \, {y} {\left(2 \, t - 3\right)} + 2 \, {y'} \hspace{2em} y( 0 )= 4 \, e^{4}"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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=%20-2%20%5C,%20%7By%7D%20%7B%5Cleft(2%20%5C,%20t%20-%203%5Cright)%7D%20+%202%20%5C,%20%7By'%7D%20%5Chspace%7B2em%7D%20y(%200%20)=%204%20%5C,%20e%5E%7B4%7D" alt="0 = -2 \, {y} {\left(2 \, t - 3\right)} + 2 \, {y'} \hspace{2em} y( 0 )= 4 \, e^{4}" title="0 = -2 \, {y} {\left(2 \, t - 3\right)} + 2 \, {y'} \hspace{2em} y( 0 )= 4 \, e^{4}" data-latex="0 = -2 \, {y} {\left(2 \, t - 3\right)} + 2 \, {y'} \hspace{2em} y( 0 )= 4 \, e^{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} = 4 \, e^{\left(t^{2} - 3 \, t + 4\right)}" alt="{y} = 4 \, e^{\left(t^{2} - 3 \, t + 4\right)}" title="{y} = 4 \, e^{\left(t^{2} - 3 \, t + 4\right)}" data-latex="{y} = 4 \, e^{\left(t^{2} - 3 \, t + 4\right)}"/></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,%20e%5E%7B%5Cleft(t%5E%7B2%7D%20-%203%20%5C,%20t%20+%204%5Cright)%7D" alt="{y} = 4 \, e^{\left(t^{2} - 3 \, t + 4\right)}" title="{y} = 4 \, e^{\left(t^{2} - 3 \, t + 4\right)}" data-latex="{y} = 4 \, e^{\left(t^{2} - 3 \, t + 4\right)}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-9297" title="F2 | Separation of variables | ver. 9297"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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 = -2 \, {y} {\left(4 \, t - 1\right)} + 2 \, {y'} \hspace{2em} y( 0 )= 1" alt="0 = -2 \, {y} {\left(4 \, t - 1\right)} + 2 \, {y'} \hspace{2em} y( 0 )= 1" title="0 = -2 \, {y} {\left(4 \, t - 1\right)} + 2 \, {y'} \hspace{2em} y( 0 )= 1" data-latex="0 = -2 \, {y} {\left(4 \, t - 1\right)} + 2 \, {y'} \hspace{2em} y( 0 )= 1"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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=%20-2%20%5C,%20%7By%7D%20%7B%5Cleft(4%20%5C,%20t%20-%201%5Cright)%7D%20+%202%20%5C,%20%7By'%7D%20%5Chspace%7B2em%7D%20y(%200%20)=%201" alt="0 = -2 \, {y} {\left(4 \, t - 1\right)} + 2 \, {y'} \hspace{2em} y( 0 )= 1" title="0 = -2 \, {y} {\left(4 \, t - 1\right)} + 2 \, {y'} \hspace{2em} y( 0 )= 1" data-latex="0 = -2 \, {y} {\left(4 \, t - 1\right)} + 2 \, {y'} \hspace{2em} y( 0 )= 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} = e^{\left(2 \, t^{2} - t\right)}" alt="{y} = e^{\left(2 \, t^{2} - t\right)}" title="{y} = e^{\left(2 \, t^{2} - t\right)}" data-latex="{y} = e^{\left(2 \, t^{2} - t\right)}"/></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=%20e%5E%7B%5Cleft(2%20%5C,%20t%5E%7B2%7D%20-%20t%5Cright)%7D" alt="{y} = e^{\left(2 \, t^{2} - t\right)}" title="{y} = e^{\left(2 \, t^{2} - t\right)}" data-latex="{y} = e^{\left(2 \, t^{2} - t\right)}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-7958" title="F2 | Separation of variables | ver. 7958"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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 \, {y} \sin\left(t\right) = -2 \, {y'} \hspace{2em} y( 0 )= 2 \, e^{3}" alt="6 \, {y} \sin\left(t\right) = -2 \, {y'} \hspace{2em} y( 0 )= 2 \, e^{3}" title="6 \, {y} \sin\left(t\right) = -2 \, {y'} \hspace{2em} y( 0 )= 2 \, e^{3}" data-latex="6 \, {y} \sin\left(t\right) = -2 \, {y'} \hspace{2em} y( 0 )= 2 \, e^{3}"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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,%20%7By%7D%20%5Csin%5Cleft(t%5Cright)%20=%20-2%20%5C,%20%7By'%7D%20%5Chspace%7B2em%7D%20y(%200%20)=%202%20%5C,%20e%5E%7B3%7D" alt="6 \, {y} \sin\left(t\right) = -2 \, {y'} \hspace{2em} y( 0 )= 2 \, e^{3}" title="6 \, {y} \sin\left(t\right) = -2 \, {y'} \hspace{2em} y( 0 )= 2 \, e^{3}" data-latex="6 \, {y} \sin\left(t\right) = -2 \, {y'} \hspace{2em} y( 0 )= 2 \, e^{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 \, e^{\left(3 \, \cos\left(t\right)\right)}" alt="{y} = 2 \, e^{\left(3 \, \cos\left(t\right)\right)}" title="{y} = 2 \, e^{\left(3 \, \cos\left(t\right)\right)}" data-latex="{y} = 2 \, e^{\left(3 \, \cos\left(t\right)\right)}"/></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,%20e%5E%7B%5Cleft(3%20%5C,%20%5Ccos%5Cleft(t%5Cright)%5Cright)%7D" alt="{y} = 2 \, e^{\left(3 \, \cos\left(t\right)\right)}" title="{y} = 2 \, e^{\left(3 \, \cos\left(t\right)\right)}" data-latex="{y} = 2 \, e^{\left(3 \, \cos\left(t\right)\right)}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-9272" title="F2 | Separation of variables | ver. 9272"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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'} = 2 \, {y} \cos\left(t\right) \hspace{2em} y( 0 )= 1" alt="-2 \, {y'} = 2 \, {y} \cos\left(t\right) \hspace{2em} y( 0 )= 1" title="-2 \, {y'} = 2 \, {y} \cos\left(t\right) \hspace{2em} y( 0 )= 1" data-latex="-2 \, {y'} = 2 \, {y} \cos\left(t\right) \hspace{2em} y( 0 )= 1"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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=%202%20%5C,%20%7By%7D%20%5Ccos%5Cleft(t%5Cright)%20%5Chspace%7B2em%7D%20y(%200%20)=%201" alt="-2 \, {y'} = 2 \, {y} \cos\left(t\right) \hspace{2em} y( 0 )= 1" title="-2 \, {y'} = 2 \, {y} \cos\left(t\right) \hspace{2em} y( 0 )= 1" data-latex="-2 \, {y'} = 2 \, {y} \cos\left(t\right) \hspace{2em} y( 0 )= 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} = e^{\left(-\sin\left(t\right)\right)}" alt="{y} = e^{\left(-\sin\left(t\right)\right)}" title="{y} = e^{\left(-\sin\left(t\right)\right)}" data-latex="{y} = e^{\left(-\sin\left(t\right)\right)}"/></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=%20e%5E%7B%5Cleft(-%5Csin%5Cleft(t%5Cright)%5Cright)%7D" alt="{y} = e^{\left(-\sin\left(t\right)\right)}" title="{y} = e^{\left(-\sin\left(t\right)\right)}" data-latex="{y} = e^{\left(-\sin\left(t\right)\right)}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-8449" title="F2 | Separation of variables | ver. 8449"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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 \, {\left(4 \, t - 3\right)} {y} - 3 \, {y'} = 0 \hspace{2em} y( 0 )= -4 \, e^{3}" alt="-3 \, {\left(4 \, t - 3\right)} {y} - 3 \, {y'} = 0 \hspace{2em} y( 0 )= -4 \, e^{3}" title="-3 \, {\left(4 \, t - 3\right)} {y} - 3 \, {y'} = 0 \hspace{2em} y( 0 )= -4 \, e^{3}" data-latex="-3 \, {\left(4 \, t - 3\right)} {y} - 3 \, {y'} = 0 \hspace{2em} y( 0 )= -4 \, e^{3}"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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%7B%5Cleft(4%20%5C,%20t%20-%203%5Cright)%7D%20%7By%7D%20-%203%20%5C,%20%7By'%7D%20=%200%20%5Chspace%7B2em%7D%20y(%200%20)=%20-4%20%5C,%20e%5E%7B3%7D" alt="-3 \, {\left(4 \, t - 3\right)} {y} - 3 \, {y'} = 0 \hspace{2em} y( 0 )= -4 \, e^{3}" title="-3 \, {\left(4 \, t - 3\right)} {y} - 3 \, {y'} = 0 \hspace{2em} y( 0 )= -4 \, e^{3}" data-latex="-3 \, {\left(4 \, t - 3\right)} {y} - 3 \, {y'} = 0 \hspace{2em} y( 0 )= -4 \, e^{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} = -4 \, e^{\left(-2 \, t^{2} + 3 \, t + 3\right)}" alt="{y} = -4 \, e^{\left(-2 \, t^{2} + 3 \, t + 3\right)}" title="{y} = -4 \, e^{\left(-2 \, t^{2} + 3 \, t + 3\right)}" data-latex="{y} = -4 \, e^{\left(-2 \, t^{2} + 3 \, t + 3\right)}"/></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,%20e%5E%7B%5Cleft(-2%20%5C,%20t%5E%7B2%7D%20+%203%20%5C,%20t%20+%203%5Cright)%7D" alt="{y} = -4 \, e^{\left(-2 \, t^{2} + 3 \, t + 3\right)}" title="{y} = -4 \, e^{\left(-2 \, t^{2} + 3 \, t + 3\right)}" data-latex="{y} = -4 \, e^{\left(-2 \, t^{2} + 3 \, t + 3\right)}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-5606" title="F2 | Separation of variables | ver. 5606"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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} = \frac{6 \, t}{{y}^{2}} + \frac{9}{{y}^{2}} \hspace{2em} y( -2 )= 4" alt="3 \, {y'} {y} = \frac{6 \, t}{{y}^{2}} + \frac{9}{{y}^{2}} \hspace{2em} y( -2 )= 4" title="3 \, {y'} {y} = \frac{6 \, t}{{y}^{2}} + \frac{9}{{y}^{2}} \hspace{2em} y( -2 )= 4" data-latex="3 \, {y'} {y} = \frac{6 \, t}{{y}^{2}} + \frac{9}{{y}^{2}} \hspace{2em} y( -2 )= 4"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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%7By%7D%20=%20%5Cfrac%7B6%20%5C,%20t%7D%7B%7By%7D%5E%7B2%7D%7D%20+%20%5Cfrac%7B9%7D%7B%7By%7D%5E%7B2%7D%7D%20%5Chspace%7B2em%7D%20y(%20-2%20)=%204" alt="3 \, {y'} {y} = \frac{6 \, t}{{y}^{2}} + \frac{9}{{y}^{2}} \hspace{2em} y( -2 )= 4" title="3 \, {y'} {y} = \frac{6 \, t}{{y}^{2}} + \frac{9}{{y}^{2}} \hspace{2em} y( -2 )= 4" data-latex="3 \, {y'} {y} = \frac{6 \, t}{{y}^{2}} + \frac{9}{{y}^{2}} \hspace{2em} y( -2 )= 4"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y} = {\left(t^{2} + 3 \, t + 66\right)}^{\frac{1}{3}}" alt="{y} = {\left(t^{2} + 3 \, t + 66\right)}^{\frac{1}{3}}" title="{y} = {\left(t^{2} + 3 \, t + 66\right)}^{\frac{1}{3}}" data-latex="{y} = {\left(t^{2} + 3 \, t + 66\right)}^{\frac{1}{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%7B%5Cleft(t%5E%7B2%7D%20+%203%20%5C,%20t%20+%2066%5Cright)%7D%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D" alt="{y} = {\left(t^{2} + 3 \, t + 66\right)}^{\frac{1}{3}}" title="{y} = {\left(t^{2} + 3 \, t + 66\right)}^{\frac{1}{3}}" data-latex="{y} = {\left(t^{2} + 3 \, t + 66\right)}^{\frac{1}{3}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-1314" title="F2 | Separation of variables | ver. 1314"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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{4 \, t}{{y}} = -2 \, {y} {y'} + \frac{6}{{y}} \hspace{2em} y( -3 )= 4" alt="-\frac{4 \, t}{{y}} = -2 \, {y} {y'} + \frac{6}{{y}} \hspace{2em} y( -3 )= 4" title="-\frac{4 \, t}{{y}} = -2 \, {y} {y'} + \frac{6}{{y}} \hspace{2em} y( -3 )= 4" data-latex="-\frac{4 \, t}{{y}} = -2 \, {y} {y'} + \frac{6}{{y}} \hspace{2em} y( -3 )= 4"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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%7B4%20%5C,%20t%7D%7B%7By%7D%7D%20=%20-2%20%5C,%20%7By%7D%20%7By'%7D%20+%20%5Cfrac%7B6%7D%7B%7By%7D%7D%20%5Chspace%7B2em%7D%20y(%20-3%20)=%204" alt="-\frac{4 \, t}{{y}} = -2 \, {y} {y'} + \frac{6}{{y}} \hspace{2em} y( -3 )= 4" title="-\frac{4 \, t}{{y}} = -2 \, {y} {y'} + \frac{6}{{y}} \hspace{2em} y( -3 )= 4" data-latex="-\frac{4 \, t}{{y}} = -2 \, {y} {y'} + \frac{6}{{y}} \hspace{2em} y( -3 )= 4"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y} = \sqrt{t^{2} + 3 \, t + 16}" alt="{y} = \sqrt{t^{2} + 3 \, t + 16}" title="{y} = \sqrt{t^{2} + 3 \, t + 16}" data-latex="{y} = \sqrt{t^{2} + 3 \, t + 16}"/></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%5Csqrt%7Bt%5E%7B2%7D%20+%203%20%5C,%20t%20+%2016%7D" alt="{y} = \sqrt{t^{2} + 3 \, t + 16}" title="{y} = \sqrt{t^{2} + 3 \, t + 16}" data-latex="{y} = \sqrt{t^{2} + 3 \, t + 16}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-0849" title="F2 | Separation of variables | ver. 0849"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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 = 6 \, {y} \cos\left(t\right) + 3 \, {y'} \hspace{2em} y( 0 )= 2" alt="0 = 6 \, {y} \cos\left(t\right) + 3 \, {y'} \hspace{2em} y( 0 )= 2" title="0 = 6 \, {y} \cos\left(t\right) + 3 \, {y'} \hspace{2em} y( 0 )= 2" data-latex="0 = 6 \, {y} \cos\left(t\right) + 3 \, {y'} \hspace{2em} y( 0 )= 2"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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=%206%20%5C,%20%7By%7D%20%5Ccos%5Cleft(t%5Cright)%20+%203%20%5C,%20%7By'%7D%20%5Chspace%7B2em%7D%20y(%200%20)=%202" alt="0 = 6 \, {y} \cos\left(t\right) + 3 \, {y'} \hspace{2em} y( 0 )= 2" title="0 = 6 \, {y} \cos\left(t\right) + 3 \, {y'} \hspace{2em} y( 0 )= 2" data-latex="0 = 6 \, {y} \cos\left(t\right) + 3 \, {y'} \hspace{2em} y( 0 )= 2"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y} = 2 \, e^{\left(-2 \, \sin\left(t\right)\right)}" alt="{y} = 2 \, e^{\left(-2 \, \sin\left(t\right)\right)}" title="{y} = 2 \, e^{\left(-2 \, \sin\left(t\right)\right)}" data-latex="{y} = 2 \, e^{\left(-2 \, \sin\left(t\right)\right)}"/></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,%20e%5E%7B%5Cleft(-2%20%5C,%20%5Csin%5Cleft(t%5Cright)%5Cright)%7D" alt="{y} = 2 \, e^{\left(-2 \, \sin\left(t\right)\right)}" title="{y} = 2 \, e^{\left(-2 \, \sin\left(t\right)\right)}" data-latex="{y} = 2 \, e^{\left(-2 \, \sin\left(t\right)\right)}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-3230" title="F2 | Separation of variables | ver. 3230"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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'} t = -9 \, {y} \hspace{2em} y( -4 )= \frac{1}{64}" alt="3 \, {y'} t = -9 \, {y} \hspace{2em} y( -4 )= \frac{1}{64}" title="3 \, {y'} t = -9 \, {y} \hspace{2em} y( -4 )= \frac{1}{64}" data-latex="3 \, {y'} t = -9 \, {y} \hspace{2em} y( -4 )= \frac{1}{64}"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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%20t%20=%20-9%20%5C,%20%7By%7D%20%5Chspace%7B2em%7D%20y(%20-4%20)=%20%5Cfrac%7B1%7D%7B64%7D" alt="3 \, {y'} t = -9 \, {y} \hspace{2em} y( -4 )= \frac{1}{64}" title="3 \, {y'} t = -9 \, {y} \hspace{2em} y( -4 )= \frac{1}{64}" data-latex="3 \, {y'} t = -9 \, {y} \hspace{2em} y( -4 )= \frac{1}{64}"&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}}" alt="{y} = -\frac{1}{t^{3}}" title="{y} = -\frac{1}{t^{3}}" data-latex="{y} = -\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%7B3%7D%7D" alt="{y} = -\frac{1}{t^{3}}" title="{y} = -\frac{1}{t^{3}}" data-latex="{y} = -\frac{1}{t^{3}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-1113" title="F2 | Separation of variables | ver. 1113"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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 = 6 \, {y} {\left(2 \, t - 1\right)} - 3 \, {y'} \hspace{2em} y( 0 )= -3 \, e^{5}" alt="0 = 6 \, {y} {\left(2 \, t - 1\right)} - 3 \, {y'} \hspace{2em} y( 0 )= -3 \, e^{5}" title="0 = 6 \, {y} {\left(2 \, t - 1\right)} - 3 \, {y'} \hspace{2em} y( 0 )= -3 \, e^{5}" data-latex="0 = 6 \, {y} {\left(2 \, t - 1\right)} - 3 \, {y'} \hspace{2em} y( 0 )= -3 \, e^{5}"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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=%206%20%5C,%20%7By%7D%20%7B%5Cleft(2%20%5C,%20t%20-%201%5Cright)%7D%20-%203%20%5C,%20%7By'%7D%20%5Chspace%7B2em%7D%20y(%200%20)=%20-3%20%5C,%20e%5E%7B5%7D" alt="0 = 6 \, {y} {\left(2 \, t - 1\right)} - 3 \, {y'} \hspace{2em} y( 0 )= -3 \, e^{5}" title="0 = 6 \, {y} {\left(2 \, t - 1\right)} - 3 \, {y'} \hspace{2em} y( 0 )= -3 \, e^{5}" data-latex="0 = 6 \, {y} {\left(2 \, t - 1\right)} - 3 \, {y'} \hspace{2em} y( 0 )= -3 \, e^{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} = -3 \, e^{\left(2 \, t^{2} - 2 \, t + 5\right)}" alt="{y} = -3 \, e^{\left(2 \, t^{2} - 2 \, t + 5\right)}" title="{y} = -3 \, e^{\left(2 \, t^{2} - 2 \, t + 5\right)}" data-latex="{y} = -3 \, e^{\left(2 \, t^{2} - 2 \, t + 5\right)}"/></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,%20e%5E%7B%5Cleft(2%20%5C,%20t%5E%7B2%7D%20-%202%20%5C,%20t%20+%205%5Cright)%7D" alt="{y} = -3 \, e^{\left(2 \, t^{2} - 2 \, t + 5\right)}" title="{y} = -3 \, e^{\left(2 \, t^{2} - 2 \, t + 5\right)}" data-latex="{y} = -3 \, e^{\left(2 \, t^{2} - 2 \, t + 5\right)}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-3578" title="F2 | Separation of variables | ver. 3578"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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 \, {y} {\left(2 \, t - 1\right)} \hspace{2em} y( 0 )= 3 \, e^{5}" alt="-3 \, {y'} = -6 \, {y} {\left(2 \, t - 1\right)} \hspace{2em} y( 0 )= 3 \, e^{5}" title="-3 \, {y'} = -6 \, {y} {\left(2 \, t - 1\right)} \hspace{2em} y( 0 )= 3 \, e^{5}" data-latex="-3 \, {y'} = -6 \, {y} {\left(2 \, t - 1\right)} \hspace{2em} y( 0 )= 3 \, e^{5}"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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=%20-6%20%5C,%20%7By%7D%20%7B%5Cleft(2%20%5C,%20t%20-%201%5Cright)%7D%20%5Chspace%7B2em%7D%20y(%200%20)=%203%20%5C,%20e%5E%7B5%7D" alt="-3 \, {y'} = -6 \, {y} {\left(2 \, t - 1\right)} \hspace{2em} y( 0 )= 3 \, e^{5}" title="-3 \, {y'} = -6 \, {y} {\left(2 \, t - 1\right)} \hspace{2em} y( 0 )= 3 \, e^{5}" data-latex="-3 \, {y'} = -6 \, {y} {\left(2 \, t - 1\right)} \hspace{2em} y( 0 )= 3 \, e^{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} = 3 \, e^{\left(2 \, t^{2} - 2 \, t + 5\right)}" alt="{y} = 3 \, e^{\left(2 \, t^{2} - 2 \, t + 5\right)}" title="{y} = 3 \, e^{\left(2 \, t^{2} - 2 \, t + 5\right)}" data-latex="{y} = 3 \, e^{\left(2 \, t^{2} - 2 \, t + 5\right)}"/></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,%20e%5E%7B%5Cleft(2%20%5C,%20t%5E%7B2%7D%20-%202%20%5C,%20t%20+%205%5Cright)%7D" alt="{y} = 3 \, e^{\left(2 \, t^{2} - 2 \, t + 5\right)}" title="{y} = 3 \, e^{\left(2 \, t^{2} - 2 \, t + 5\right)}" data-latex="{y} = 3 \, e^{\left(2 \, t^{2} - 2 \, t + 5\right)}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-9927" title="F2 | Separation of variables | ver. 9927"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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 = -3 \, t {y'} + 9 \, {y} \hspace{2em} y( -2 )= -32" alt="0 = -3 \, t {y'} + 9 \, {y} \hspace{2em} y( -2 )= -32" title="0 = -3 \, t {y'} + 9 \, {y} \hspace{2em} y( -2 )= -32" data-latex="0 = -3 \, t {y'} + 9 \, {y} \hspace{2em} y( -2 )= -32"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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=%20-3%20%5C,%20t%20%7By'%7D%20+%209%20%5C,%20%7By%7D%20%5Chspace%7B2em%7D%20y(%20-2%20)=%20-32" alt="0 = -3 \, t {y'} + 9 \, {y} \hspace{2em} y( -2 )= -32" title="0 = -3 \, t {y'} + 9 \, {y} \hspace{2em} y( -2 )= -32" data-latex="0 = -3 \, t {y'} + 9 \, {y} \hspace{2em} y( -2 )= -32"&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}" alt="{y} = 4 \, t^{3}" title="{y} = 4 \, t^{3}" data-latex="{y} = 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=%204%20%5C,%20t%5E%7B3%7D" alt="{y} = 4 \, t^{3}" title="{y} = 4 \, t^{3}" data-latex="{y} = 4 \, t^{3}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-1700" title="F2 | Separation of variables | ver. 1700"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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'} t = -9 \, {y} \hspace{2em} y( 1 )= -2" alt="-3 \, {y'} t = -9 \, {y} \hspace{2em} y( 1 )= -2" title="-3 \, {y'} t = -9 \, {y} \hspace{2em} y( 1 )= -2" data-latex="-3 \, {y'} t = -9 \, {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;F2.&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%20t%20=%20-9%20%5C,%20%7By%7D%20%5Chspace%7B2em%7D%20y(%201%20)=%20-2" alt="-3 \, {y'} t = -9 \, {y} \hspace{2em} y( 1 )= -2" title="-3 \, {y'} t = -9 \, {y} \hspace{2em} y( 1 )= -2" data-latex="-3 \, {y'} t = -9 \, {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^{3}" alt="{y} = -2 \, t^{3}" title="{y} = -2 \, t^{3}" data-latex="{y} = -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=%20-2%20%5C,%20t%5E%7B3%7D" alt="{y} = -2 \, t^{3}" title="{y} = -2 \, t^{3}" data-latex="{y} = -2 \, t^{3}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-7934" title="F2 | Separation of variables | ver. 7934"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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'} {y} - \frac{6}{{y}} = \frac{4 \, t}{{y}} \hspace{2em} y( 3 )= 3" alt="2 \, {y'} {y} - \frac{6}{{y}} = \frac{4 \, t}{{y}} \hspace{2em} y( 3 )= 3" title="2 \, {y'} {y} - \frac{6}{{y}} = \frac{4 \, t}{{y}} \hspace{2em} y( 3 )= 3" data-latex="2 \, {y'} {y} - \frac{6}{{y}} = \frac{4 \, t}{{y}} \hspace{2em} y( 3 )= 3"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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%7By%7D%20-%20%5Cfrac%7B6%7D%7B%7By%7D%7D%20=%20%5Cfrac%7B4%20%5C,%20t%7D%7B%7By%7D%7D%20%5Chspace%7B2em%7D%20y(%203%20)=%203" alt="2 \, {y'} {y} - \frac{6}{{y}} = \frac{4 \, t}{{y}} \hspace{2em} y( 3 )= 3" title="2 \, {y'} {y} - \frac{6}{{y}} = \frac{4 \, t}{{y}} \hspace{2em} y( 3 )= 3" data-latex="2 \, {y'} {y} - \frac{6}{{y}} = \frac{4 \, t}{{y}} \hspace{2em} y( 3 )= 3"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y} = \sqrt{t^{2} + 3 \, t - 9}" alt="{y} = \sqrt{t^{2} + 3 \, t - 9}" title="{y} = \sqrt{t^{2} + 3 \, t - 9}" data-latex="{y} = \sqrt{t^{2} + 3 \, t - 9}"/></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%5Csqrt%7Bt%5E%7B2%7D%20+%203%20%5C,%20t%20-%209%7D" alt="{y} = \sqrt{t^{2} + 3 \, t - 9}" title="{y} = \sqrt{t^{2} + 3 \, t - 9}" data-latex="{y} = \sqrt{t^{2} + 3 \, t - 9}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-4639" title="F2 | Separation of variables | ver. 4639"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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 + 4 \, {y} = 0 \hspace{2em} y( -4 )= 32" alt="-2 \, {y'} t + 4 \, {y} = 0 \hspace{2em} y( -4 )= 32" title="-2 \, {y'} t + 4 \, {y} = 0 \hspace{2em} y( -4 )= 32" data-latex="-2 \, {y'} t + 4 \, {y} = 0 \hspace{2em} y( -4 )= 32"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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%20t%20+%204%20%5C,%20%7By%7D%20=%200%20%5Chspace%7B2em%7D%20y(%20-4%20)=%2032" alt="-2 \, {y'} t + 4 \, {y} = 0 \hspace{2em} y( -4 )= 32" title="-2 \, {y'} t + 4 \, {y} = 0 \hspace{2em} y( -4 )= 32" data-latex="-2 \, {y'} t + 4 \, {y} = 0 \hspace{2em} y( -4 )= 32"&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}" alt="{y} = 2 \, t^{2}" title="{y} = 2 \, t^{2}" data-latex="{y} = 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=%202%20%5C,%20t%5E%7B2%7D" alt="{y} = 2 \, t^{2}" title="{y} = 2 \, t^{2}" data-latex="{y} = 2 \, t^{2}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-1496" title="F2 | Separation of variables | ver. 1496"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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 \, {y} \sin\left(t\right) = 2 \, {y'} \hspace{2em} y( 0 )= -2 \, e^{3}" alt="-6 \, {y} \sin\left(t\right) = 2 \, {y'} \hspace{2em} y( 0 )= -2 \, e^{3}" title="-6 \, {y} \sin\left(t\right) = 2 \, {y'} \hspace{2em} y( 0 )= -2 \, e^{3}" data-latex="-6 \, {y} \sin\left(t\right) = 2 \, {y'} \hspace{2em} y( 0 )= -2 \, e^{3}"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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,%20%7By%7D%20%5Csin%5Cleft(t%5Cright)%20=%202%20%5C,%20%7By'%7D%20%5Chspace%7B2em%7D%20y(%200%20)=%20-2%20%5C,%20e%5E%7B3%7D" alt="-6 \, {y} \sin\left(t\right) = 2 \, {y'} \hspace{2em} y( 0 )= -2 \, e^{3}" title="-6 \, {y} \sin\left(t\right) = 2 \, {y'} \hspace{2em} y( 0 )= -2 \, e^{3}" data-latex="-6 \, {y} \sin\left(t\right) = 2 \, {y'} \hspace{2em} y( 0 )= -2 \, e^{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 \, e^{\left(3 \, \cos\left(t\right)\right)}" alt="{y} = -2 \, e^{\left(3 \, \cos\left(t\right)\right)}" title="{y} = -2 \, e^{\left(3 \, \cos\left(t\right)\right)}" data-latex="{y} = -2 \, e^{\left(3 \, \cos\left(t\right)\right)}"/></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,%20e%5E%7B%5Cleft(3%20%5C,%20%5Ccos%5Cleft(t%5Cright)%5Cright)%7D" alt="{y} = -2 \, e^{\left(3 \, \cos\left(t\right)\right)}" title="{y} = -2 \, e^{\left(3 \, \cos\left(t\right)\right)}" data-latex="{y} = -2 \, e^{\left(3 \, \cos\left(t\right)\right)}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-6320" title="F2 | Separation of variables | ver. 6320"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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 {y'} = 6 \, {y} \hspace{2em} y( -4 )= -\frac{1}{16}" alt="-2 \, t {y'} = 6 \, {y} \hspace{2em} y( -4 )= -\frac{1}{16}" title="-2 \, t {y'} = 6 \, {y} \hspace{2em} y( -4 )= -\frac{1}{16}" data-latex="-2 \, t {y'} = 6 \, {y} \hspace{2em} y( -4 )= -\frac{1}{16}"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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%20%7By'%7D%20=%206%20%5C,%20%7By%7D%20%5Chspace%7B2em%7D%20y(%20-4%20)=%20-%5Cfrac%7B1%7D%7B16%7D" alt="-2 \, t {y'} = 6 \, {y} \hspace{2em} y( -4 )= -\frac{1}{16}" title="-2 \, t {y'} = 6 \, {y} \hspace{2em} y( -4 )= -\frac{1}{16}" data-latex="-2 \, t {y'} = 6 \, {y} \hspace{2em} y( -4 )= -\frac{1}{16}"&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^{3}}" alt="{y} = \frac{4}{t^{3}}" title="{y} = \frac{4}{t^{3}}" data-latex="{y} = \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%5Cfrac%7B4%7D%7Bt%5E%7B3%7D%7D" alt="{y} = \frac{4}{t^{3}}" title="{y} = \frac{4}{t^{3}}" data-latex="{y} = \frac{4}{t^{3}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-1999" title="F2 | Separation of variables | ver. 1999"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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 \, {\left(6 \, t - 1\right)} {y} - 2 \, {y'} = 0 \hspace{2em} y( 0 )= 2 \, e^{\left(-5\right)}" alt="2 \, {\left(6 \, t - 1\right)} {y} - 2 \, {y'} = 0 \hspace{2em} y( 0 )= 2 \, e^{\left(-5\right)}" title="2 \, {\left(6 \, t - 1\right)} {y} - 2 \, {y'} = 0 \hspace{2em} y( 0 )= 2 \, e^{\left(-5\right)}" data-latex="2 \, {\left(6 \, t - 1\right)} {y} - 2 \, {y'} = 0 \hspace{2em} y( 0 )= 2 \, e^{\left(-5\right)}"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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%7B%5Cleft(6%20%5C,%20t%20-%201%5Cright)%7D%20%7By%7D%20-%202%20%5C,%20%7By'%7D%20=%200%20%5Chspace%7B2em%7D%20y(%200%20)=%202%20%5C,%20e%5E%7B%5Cleft(-5%5Cright)%7D" alt="2 \, {\left(6 \, t - 1\right)} {y} - 2 \, {y'} = 0 \hspace{2em} y( 0 )= 2 \, e^{\left(-5\right)}" title="2 \, {\left(6 \, t - 1\right)} {y} - 2 \, {y'} = 0 \hspace{2em} y( 0 )= 2 \, e^{\left(-5\right)}" data-latex="2 \, {\left(6 \, t - 1\right)} {y} - 2 \, {y'} = 0 \hspace{2em} y( 0 )= 2 \, e^{\left(-5\right)}"&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 \, e^{\left(3 \, t^{2} - t - 5\right)}" alt="{y} = 2 \, e^{\left(3 \, t^{2} - t - 5\right)}" title="{y} = 2 \, e^{\left(3 \, t^{2} - t - 5\right)}" data-latex="{y} = 2 \, e^{\left(3 \, t^{2} - t - 5\right)}"/></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,%20e%5E%7B%5Cleft(3%20%5C,%20t%5E%7B2%7D%20-%20t%20-%205%5Cright)%7D" alt="{y} = 2 \, e^{\left(3 \, t^{2} - t - 5\right)}" title="{y} = 2 \, e^{\left(3 \, t^{2} - t - 5\right)}" data-latex="{y} = 2 \, e^{\left(3 \, t^{2} - t - 5\right)}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-8809" title="F2 | Separation of variables | ver. 8809"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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} = -2 \, t {y'} \hspace{2em} y( -1 )= 4" alt="-4 \, {y} = -2 \, t {y'} \hspace{2em} y( -1 )= 4" title="-4 \, {y} = -2 \, t {y'} \hspace{2em} y( -1 )= 4" data-latex="-4 \, {y} = -2 \, 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;F2.&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=%20-2%20%5C,%20t%20%7By'%7D%20%5Chspace%7B2em%7D%20y(%20-1%20)=%204" alt="-4 \, {y} = -2 \, t {y'} \hspace{2em} y( -1 )= 4" title="-4 \, {y} = -2 \, t {y'} \hspace{2em} y( -1 )= 4" data-latex="-4 \, {y} = -2 \, 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} = 4 \, t^{2}" alt="{y} = 4 \, t^{2}" title="{y} = 4 \, t^{2}" data-latex="{y} = 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=%204%20%5C,%20t%5E%7B2%7D" alt="{y} = 4 \, t^{2}" title="{y} = 4 \, t^{2}" data-latex="{y} = 4 \, t^{2}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-8247" title="F2 | Separation of variables | ver. 8247"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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 \, {y} = 2 \, t {y'} \hspace{2em} y( -1 )= -3" alt="-6 \, {y} = 2 \, t {y'} \hspace{2em} y( -1 )= -3" title="-6 \, {y} = 2 \, t {y'} \hspace{2em} y( -1 )= -3" data-latex="-6 \, {y} = 2 \, t {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;F2.&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,%20%7By%7D%20=%202%20%5C,%20t%20%7By'%7D%20%5Chspace%7B2em%7D%20y(%20-1%20)=%20-3" alt="-6 \, {y} = 2 \, t {y'} \hspace{2em} y( -1 )= -3" title="-6 \, {y} = 2 \, t {y'} \hspace{2em} y( -1 )= -3" data-latex="-6 \, {y} = 2 \, t {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{3}{t^{3}}" alt="{y} = \frac{3}{t^{3}}" title="{y} = \frac{3}{t^{3}}" data-latex="{y} = \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%7B3%7D%7Bt%5E%7B3%7D%7D" alt="{y} = \frac{3}{t^{3}}" title="{y} = \frac{3}{t^{3}}" data-latex="{y} = \frac{3}{t^{3}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-8531" title="F2 | Separation of variables | ver. 8531"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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}{{y}^{2}} + \frac{3}{{y}^{2}} = 3 \, {y} {y'} \hspace{2em} y( -3 )= 4" alt="\frac{6 \, t}{{y}^{2}} + \frac{3}{{y}^{2}} = 3 \, {y} {y'} \hspace{2em} y( -3 )= 4" title="\frac{6 \, t}{{y}^{2}} + \frac{3}{{y}^{2}} = 3 \, {y} {y'} \hspace{2em} y( -3 )= 4" data-latex="\frac{6 \, t}{{y}^{2}} + \frac{3}{{y}^{2}} = 3 \, {y} {y'} \hspace{2em} y( -3 )= 4"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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%20%5C,%20t%7D%7B%7By%7D%5E%7B2%7D%7D%20+%20%5Cfrac%7B3%7D%7B%7By%7D%5E%7B2%7D%7D%20=%203%20%5C,%20%7By%7D%20%7By'%7D%20%5Chspace%7B2em%7D%20y(%20-3%20)=%204" alt="\frac{6 \, t}{{y}^{2}} + \frac{3}{{y}^{2}} = 3 \, {y} {y'} \hspace{2em} y( -3 )= 4" title="\frac{6 \, t}{{y}^{2}} + \frac{3}{{y}^{2}} = 3 \, {y} {y'} \hspace{2em} y( -3 )= 4" data-latex="\frac{6 \, t}{{y}^{2}} + \frac{3}{{y}^{2}} = 3 \, {y} {y'} \hspace{2em} y( -3 )= 4"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y} = {\left(t^{2} + t + 58\right)}^{\frac{1}{3}}" alt="{y} = {\left(t^{2} + t + 58\right)}^{\frac{1}{3}}" title="{y} = {\left(t^{2} + t + 58\right)}^{\frac{1}{3}}" data-latex="{y} = {\left(t^{2} + t + 58\right)}^{\frac{1}{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%7B%5Cleft(t%5E%7B2%7D%20+%20t%20+%2058%5Cright)%7D%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D" alt="{y} = {\left(t^{2} + t + 58\right)}^{\frac{1}{3}}" title="{y} = {\left(t^{2} + t + 58\right)}^{\frac{1}{3}}" data-latex="{y} = {\left(t^{2} + t + 58\right)}^{\frac{1}{3}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-9132" title="F2 | Separation of variables | ver. 9132"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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'} {y} - \frac{2}{{y}^{2}} = \frac{8 \, t}{{y}^{2}} \hspace{2em} y( -2 )= 4" alt="2 \, {y'} {y} - \frac{2}{{y}^{2}} = \frac{8 \, t}{{y}^{2}} \hspace{2em} y( -2 )= 4" title="2 \, {y'} {y} - \frac{2}{{y}^{2}} = \frac{8 \, t}{{y}^{2}} \hspace{2em} y( -2 )= 4" data-latex="2 \, {y'} {y} - \frac{2}{{y}^{2}} = \frac{8 \, t}{{y}^{2}} \hspace{2em} y( -2 )= 4"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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%7By%7D%20-%20%5Cfrac%7B2%7D%7B%7By%7D%5E%7B2%7D%7D%20=%20%5Cfrac%7B8%20%5C,%20t%7D%7B%7By%7D%5E%7B2%7D%7D%20%5Chspace%7B2em%7D%20y(%20-2%20)=%204" alt="2 \, {y'} {y} - \frac{2}{{y}^{2}} = \frac{8 \, t}{{y}^{2}} \hspace{2em} y( -2 )= 4" title="2 \, {y'} {y} - \frac{2}{{y}^{2}} = \frac{8 \, t}{{y}^{2}} \hspace{2em} y( -2 )= 4" data-latex="2 \, {y'} {y} - \frac{2}{{y}^{2}} = \frac{8 \, t}{{y}^{2}} \hspace{2em} y( -2 )= 4"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y} = {\left(2 \, t^{2} + t + 58\right)}^{\frac{1}{3}}" alt="{y} = {\left(2 \, t^{2} + t + 58\right)}^{\frac{1}{3}}" title="{y} = {\left(2 \, t^{2} + t + 58\right)}^{\frac{1}{3}}" data-latex="{y} = {\left(2 \, t^{2} + t + 58\right)}^{\frac{1}{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%7B%5Cleft(2%20%5C,%20t%5E%7B2%7D%20+%20t%20+%2058%5Cright)%7D%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D" alt="{y} = {\left(2 \, t^{2} + t + 58\right)}^{\frac{1}{3}}" title="{y} = {\left(2 \, t^{2} + t + 58\right)}^{\frac{1}{3}}" data-latex="{y} = {\left(2 \, t^{2} + t + 58\right)}^{\frac{1}{3}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-3767" title="F2 | Separation of variables | ver. 3767"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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 = -2 \, {y} {\left(4 \, t + 3\right)} + 2 \, {y'} \hspace{2em} y( 0 )= -e^{\left(-1\right)}" alt="0 = -2 \, {y} {\left(4 \, t + 3\right)} + 2 \, {y'} \hspace{2em} y( 0 )= -e^{\left(-1\right)}" title="0 = -2 \, {y} {\left(4 \, t + 3\right)} + 2 \, {y'} \hspace{2em} y( 0 )= -e^{\left(-1\right)}" data-latex="0 = -2 \, {y} {\left(4 \, t + 3\right)} + 2 \, {y'} \hspace{2em} y( 0 )= -e^{\left(-1\right)}"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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=%20-2%20%5C,%20%7By%7D%20%7B%5Cleft(4%20%5C,%20t%20+%203%5Cright)%7D%20+%202%20%5C,%20%7By'%7D%20%5Chspace%7B2em%7D%20y(%200%20)=%20-e%5E%7B%5Cleft(-1%5Cright)%7D" alt="0 = -2 \, {y} {\left(4 \, t + 3\right)} + 2 \, {y'} \hspace{2em} y( 0 )= -e^{\left(-1\right)}" title="0 = -2 \, {y} {\left(4 \, t + 3\right)} + 2 \, {y'} \hspace{2em} y( 0 )= -e^{\left(-1\right)}" data-latex="0 = -2 \, {y} {\left(4 \, t + 3\right)} + 2 \, {y'} \hspace{2em} y( 0 )= -e^{\left(-1\right)}"&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} = -e^{\left(2 \, t^{2} + 3 \, t - 1\right)}" alt="{y} = -e^{\left(2 \, t^{2} + 3 \, t - 1\right)}" title="{y} = -e^{\left(2 \, t^{2} + 3 \, t - 1\right)}" data-latex="{y} = -e^{\left(2 \, t^{2} + 3 \, t - 1\right)}"/></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-e%5E%7B%5Cleft(2%20%5C,%20t%5E%7B2%7D%20+%203%20%5C,%20t%20-%201%5Cright)%7D" alt="{y} = -e^{\left(2 \, t^{2} + 3 \, t - 1\right)}" title="{y} = -e^{\left(2 \, t^{2} + 3 \, t - 1\right)}" data-latex="{y} = -e^{\left(2 \, t^{2} + 3 \, t - 1\right)}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-8693" title="F2 | Separation of variables | ver. 8693"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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 = -3 \, t {y'} + 6 \, {y} \hspace{2em} y( -4 )= 32" alt="0 = -3 \, t {y'} + 6 \, {y} \hspace{2em} y( -4 )= 32" title="0 = -3 \, t {y'} + 6 \, {y} \hspace{2em} y( -4 )= 32" data-latex="0 = -3 \, t {y'} + 6 \, {y} \hspace{2em} y( -4 )= 32"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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=%20-3%20%5C,%20t%20%7By'%7D%20+%206%20%5C,%20%7By%7D%20%5Chspace%7B2em%7D%20y(%20-4%20)=%2032" alt="0 = -3 \, t {y'} + 6 \, {y} \hspace{2em} y( -4 )= 32" title="0 = -3 \, t {y'} + 6 \, {y} \hspace{2em} y( -4 )= 32" data-latex="0 = -3 \, t {y'} + 6 \, {y} \hspace{2em} y( -4 )= 32"&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}" alt="{y} = 2 \, t^{2}" title="{y} = 2 \, t^{2}" data-latex="{y} = 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=%202%20%5C,%20t%5E%7B2%7D" alt="{y} = 2 \, t^{2}" title="{y} = 2 \, t^{2}" data-latex="{y} = 2 \, t^{2}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-8535" title="F2 | Separation of variables | ver. 8535"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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} \sin\left(t\right) = -3 \, {y'} \hspace{2em} y( 0 )= 3 \, e^{\left(-1\right)}" alt="-3 \, {y} \sin\left(t\right) = -3 \, {y'} \hspace{2em} y( 0 )= 3 \, e^{\left(-1\right)}" title="-3 \, {y} \sin\left(t\right) = -3 \, {y'} \hspace{2em} y( 0 )= 3 \, e^{\left(-1\right)}" data-latex="-3 \, {y} \sin\left(t\right) = -3 \, {y'} \hspace{2em} y( 0 )= 3 \, e^{\left(-1\right)}"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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%5Csin%5Cleft(t%5Cright)%20=%20-3%20%5C,%20%7By'%7D%20%5Chspace%7B2em%7D%20y(%200%20)=%203%20%5C,%20e%5E%7B%5Cleft(-1%5Cright)%7D" alt="-3 \, {y} \sin\left(t\right) = -3 \, {y'} \hspace{2em} y( 0 )= 3 \, e^{\left(-1\right)}" title="-3 \, {y} \sin\left(t\right) = -3 \, {y'} \hspace{2em} y( 0 )= 3 \, e^{\left(-1\right)}" data-latex="-3 \, {y} \sin\left(t\right) = -3 \, {y'} \hspace{2em} y( 0 )= 3 \, e^{\left(-1\right)}"&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 \, e^{\left(-\cos\left(t\right)\right)}" alt="{y} = 3 \, e^{\left(-\cos\left(t\right)\right)}" title="{y} = 3 \, e^{\left(-\cos\left(t\right)\right)}" data-latex="{y} = 3 \, e^{\left(-\cos\left(t\right)\right)}"/></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,%20e%5E%7B%5Cleft(-%5Ccos%5Cleft(t%5Cright)%5Cright)%7D" alt="{y} = 3 \, e^{\left(-\cos\left(t\right)\right)}" title="{y} = 3 \, e^{\left(-\cos\left(t\right)\right)}" data-latex="{y} = 3 \, e^{\left(-\cos\left(t\right)\right)}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-7830" title="F2 | Separation of variables | ver. 7830"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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?-9 \, {y} \cos\left(t\right) + 3 \, {y'} = 0 \hspace{2em} y( 0 )= 4" alt="-9 \, {y} \cos\left(t\right) + 3 \, {y'} = 0 \hspace{2em} y( 0 )= 4" title="-9 \, {y} \cos\left(t\right) + 3 \, {y'} = 0 \hspace{2em} y( 0 )= 4" data-latex="-9 \, {y} \cos\left(t\right) + 3 \, {y'} = 0 \hspace{2em} y( 0 )= 4"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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?-9%20%5C,%20%7By%7D%20%5Ccos%5Cleft(t%5Cright)%20+%203%20%5C,%20%7By'%7D%20=%200%20%5Chspace%7B2em%7D%20y(%200%20)=%204" alt="-9 \, {y} \cos\left(t\right) + 3 \, {y'} = 0 \hspace{2em} y( 0 )= 4" title="-9 \, {y} \cos\left(t\right) + 3 \, {y'} = 0 \hspace{2em} y( 0 )= 4" data-latex="-9 \, {y} \cos\left(t\right) + 3 \, {y'} = 0 \hspace{2em} y( 0 )= 4"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y} = 4 \, e^{\left(3 \, \sin\left(t\right)\right)}" alt="{y} = 4 \, e^{\left(3 \, \sin\left(t\right)\right)}" title="{y} = 4 \, e^{\left(3 \, \sin\left(t\right)\right)}" data-latex="{y} = 4 \, e^{\left(3 \, \sin\left(t\right)\right)}"/></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,%20e%5E%7B%5Cleft(3%20%5C,%20%5Csin%5Cleft(t%5Cright)%5Cright)%7D" alt="{y} = 4 \, e^{\left(3 \, \sin\left(t\right)\right)}" title="{y} = 4 \, e^{\left(3 \, \sin\left(t\right)\right)}" data-latex="{y} = 4 \, e^{\left(3 \, \sin\left(t\right)\right)}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-8781" title="F2 | Separation of variables | ver. 8781"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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} - \frac{6 \, t}{{y}} = \frac{3}{{y}} \hspace{2em} y( 3 )= 4" alt="3 \, {y'} {y} - \frac{6 \, t}{{y}} = \frac{3}{{y}} \hspace{2em} y( 3 )= 4" title="3 \, {y'} {y} - \frac{6 \, t}{{y}} = \frac{3}{{y}} \hspace{2em} y( 3 )= 4" data-latex="3 \, {y'} {y} - \frac{6 \, t}{{y}} = \frac{3}{{y}} \hspace{2em} y( 3 )= 4"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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%7By%7D%20-%20%5Cfrac%7B6%20%5C,%20t%7D%7B%7By%7D%7D%20=%20%5Cfrac%7B3%7D%7B%7By%7D%7D%20%5Chspace%7B2em%7D%20y(%203%20)=%204" alt="3 \, {y'} {y} - \frac{6 \, t}{{y}} = \frac{3}{{y}} \hspace{2em} y( 3 )= 4" title="3 \, {y'} {y} - \frac{6 \, t}{{y}} = \frac{3}{{y}} \hspace{2em} y( 3 )= 4" data-latex="3 \, {y'} {y} - \frac{6 \, t}{{y}} = \frac{3}{{y}} \hspace{2em} y( 3 )= 4"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y} = \sqrt{t^{2} + t + 4}" alt="{y} = \sqrt{t^{2} + t + 4}" title="{y} = \sqrt{t^{2} + t + 4}" data-latex="{y} = \sqrt{t^{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%5Csqrt%7Bt%5E%7B2%7D%20+%20t%20+%204%7D" alt="{y} = \sqrt{t^{2} + t + 4}" title="{y} = \sqrt{t^{2} + t + 4}" data-latex="{y} = \sqrt{t^{2} + t + 4}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-1106" title="F2 | Separation of variables | ver. 1106"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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} \sin\left(t\right) = 2 \, {y'} \hspace{2em} y( 0 )= -4 \, e^{\left(-2\right)}" alt="4 \, {y} \sin\left(t\right) = 2 \, {y'} \hspace{2em} y( 0 )= -4 \, e^{\left(-2\right)}" title="4 \, {y} \sin\left(t\right) = 2 \, {y'} \hspace{2em} y( 0 )= -4 \, e^{\left(-2\right)}" data-latex="4 \, {y} \sin\left(t\right) = 2 \, {y'} \hspace{2em} y( 0 )= -4 \, e^{\left(-2\right)}"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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%5Csin%5Cleft(t%5Cright)%20=%202%20%5C,%20%7By'%7D%20%5Chspace%7B2em%7D%20y(%200%20)=%20-4%20%5C,%20e%5E%7B%5Cleft(-2%5Cright)%7D" alt="4 \, {y} \sin\left(t\right) = 2 \, {y'} \hspace{2em} y( 0 )= -4 \, e^{\left(-2\right)}" title="4 \, {y} \sin\left(t\right) = 2 \, {y'} \hspace{2em} y( 0 )= -4 \, e^{\left(-2\right)}" data-latex="4 \, {y} \sin\left(t\right) = 2 \, {y'} \hspace{2em} y( 0 )= -4 \, e^{\left(-2\right)}"&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 \, e^{\left(-2 \, \cos\left(t\right)\right)}" alt="{y} = -4 \, e^{\left(-2 \, \cos\left(t\right)\right)}" title="{y} = -4 \, e^{\left(-2 \, \cos\left(t\right)\right)}" data-latex="{y} = -4 \, e^{\left(-2 \, \cos\left(t\right)\right)}"/></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,%20e%5E%7B%5Cleft(-2%20%5C,%20%5Ccos%5Cleft(t%5Cright)%5Cright)%7D" alt="{y} = -4 \, e^{\left(-2 \, \cos\left(t\right)\right)}" title="{y} = -4 \, e^{\left(-2 \, \cos\left(t\right)\right)}" data-latex="{y} = -4 \, e^{\left(-2 \, \cos\left(t\right)\right)}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-0415" title="F2 | Separation of variables | ver. 0415"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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'} t = -9 \, {y} \hspace{2em} y( 3 )= -\frac{1}{27}" alt="3 \, {y'} t = -9 \, {y} \hspace{2em} y( 3 )= -\frac{1}{27}" title="3 \, {y'} t = -9 \, {y} \hspace{2em} y( 3 )= -\frac{1}{27}" data-latex="3 \, {y'} t = -9 \, {y} \hspace{2em} y( 3 )= -\frac{1}{27}"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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%20t%20=%20-9%20%5C,%20%7By%7D%20%5Chspace%7B2em%7D%20y(%203%20)=%20-%5Cfrac%7B1%7D%7B27%7D" alt="3 \, {y'} t = -9 \, {y} \hspace{2em} y( 3 )= -\frac{1}{27}" title="3 \, {y'} t = -9 \, {y} \hspace{2em} y( 3 )= -\frac{1}{27}" data-latex="3 \, {y'} t = -9 \, {y} \hspace{2em} y( 3 )= -\frac{1}{27}"&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}}" alt="{y} = -\frac{1}{t^{3}}" title="{y} = -\frac{1}{t^{3}}" data-latex="{y} = -\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%7B3%7D%7D" alt="{y} = -\frac{1}{t^{3}}" title="{y} = -\frac{1}{t^{3}}" data-latex="{y} = -\frac{1}{t^{3}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-0222" title="F2 | Separation of variables | ver. 0222"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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'} = -6 \, {y} \sin\left(t\right) \hspace{2em} y( 0 )= -2 \, e^{\left(-3\right)}" alt="-2 \, {y'} = -6 \, {y} \sin\left(t\right) \hspace{2em} y( 0 )= -2 \, e^{\left(-3\right)}" title="-2 \, {y'} = -6 \, {y} \sin\left(t\right) \hspace{2em} y( 0 )= -2 \, e^{\left(-3\right)}" data-latex="-2 \, {y'} = -6 \, {y} \sin\left(t\right) \hspace{2em} y( 0 )= -2 \, e^{\left(-3\right)}"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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=%20-6%20%5C,%20%7By%7D%20%5Csin%5Cleft(t%5Cright)%20%5Chspace%7B2em%7D%20y(%200%20)=%20-2%20%5C,%20e%5E%7B%5Cleft(-3%5Cright)%7D" alt="-2 \, {y'} = -6 \, {y} \sin\left(t\right) \hspace{2em} y( 0 )= -2 \, e^{\left(-3\right)}" title="-2 \, {y'} = -6 \, {y} \sin\left(t\right) \hspace{2em} y( 0 )= -2 \, e^{\left(-3\right)}" data-latex="-2 \, {y'} = -6 \, {y} \sin\left(t\right) \hspace{2em} y( 0 )= -2 \, e^{\left(-3\right)}"&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 \, e^{\left(-3 \, \cos\left(t\right)\right)}" alt="{y} = -2 \, e^{\left(-3 \, \cos\left(t\right)\right)}" title="{y} = -2 \, e^{\left(-3 \, \cos\left(t\right)\right)}" data-latex="{y} = -2 \, e^{\left(-3 \, \cos\left(t\right)\right)}"/></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,%20e%5E%7B%5Cleft(-3%20%5C,%20%5Ccos%5Cleft(t%5Cright)%5Cright)%7D" alt="{y} = -2 \, e^{\left(-3 \, \cos\left(t\right)\right)}" title="{y} = -2 \, e^{\left(-3 \, \cos\left(t\right)\right)}" data-latex="{y} = -2 \, e^{\left(-3 \, \cos\left(t\right)\right)}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-9889" title="F2 | Separation of variables | ver. 9889"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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 = 2 \, {y'} t - 6 \, {y} \hspace{2em} y( -3 )= -108" alt="0 = 2 \, {y'} t - 6 \, {y} \hspace{2em} y( -3 )= -108" title="0 = 2 \, {y'} t - 6 \, {y} \hspace{2em} y( -3 )= -108" data-latex="0 = 2 \, {y'} t - 6 \, {y} \hspace{2em} y( -3 )= -108"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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=%202%20%5C,%20%7By'%7D%20t%20-%206%20%5C,%20%7By%7D%20%5Chspace%7B2em%7D%20y(%20-3%20)=%20-108" alt="0 = 2 \, {y'} t - 6 \, {y} \hspace{2em} y( -3 )= -108" title="0 = 2 \, {y'} t - 6 \, {y} \hspace{2em} y( -3 )= -108" data-latex="0 = 2 \, {y'} t - 6 \, {y} \hspace{2em} y( -3 )= -108"&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}" alt="{y} = 4 \, t^{3}" title="{y} = 4 \, t^{3}" data-latex="{y} = 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=%204%20%5C,%20t%5E%7B3%7D" alt="{y} = 4 \, t^{3}" title="{y} = 4 \, t^{3}" data-latex="{y} = 4 \, t^{3}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-4310" title="F2 | Separation of variables | ver. 4310"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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} {\left(2 \, t - 1\right)} = -2 \, {y'} \hspace{2em} y( 0 )= -3 \, e^{2}" alt="4 \, {y} {\left(2 \, t - 1\right)} = -2 \, {y'} \hspace{2em} y( 0 )= -3 \, e^{2}" title="4 \, {y} {\left(2 \, t - 1\right)} = -2 \, {y'} \hspace{2em} y( 0 )= -3 \, e^{2}" data-latex="4 \, {y} {\left(2 \, t - 1\right)} = -2 \, {y'} \hspace{2em} y( 0 )= -3 \, e^{2}"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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%7B%5Cleft(2%20%5C,%20t%20-%201%5Cright)%7D%20=%20-2%20%5C,%20%7By'%7D%20%5Chspace%7B2em%7D%20y(%200%20)=%20-3%20%5C,%20e%5E%7B2%7D" alt="4 \, {y} {\left(2 \, t - 1\right)} = -2 \, {y'} \hspace{2em} y( 0 )= -3 \, e^{2}" title="4 \, {y} {\left(2 \, t - 1\right)} = -2 \, {y'} \hspace{2em} y( 0 )= -3 \, e^{2}" data-latex="4 \, {y} {\left(2 \, t - 1\right)} = -2 \, {y'} \hspace{2em} y( 0 )= -3 \, e^{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 \, e^{\left(-2 \, t^{2} + 2 \, t + 2\right)}" alt="{y} = -3 \, e^{\left(-2 \, t^{2} + 2 \, t + 2\right)}" title="{y} = -3 \, e^{\left(-2 \, t^{2} + 2 \, t + 2\right)}" data-latex="{y} = -3 \, e^{\left(-2 \, t^{2} + 2 \, t + 2\right)}"/></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,%20e%5E%7B%5Cleft(-2%20%5C,%20t%5E%7B2%7D%20+%202%20%5C,%20t%20+%202%5Cright)%7D" alt="{y} = -3 \, e^{\left(-2 \, t^{2} + 2 \, t + 2\right)}" title="{y} = -3 \, e^{\left(-2 \, t^{2} + 2 \, t + 2\right)}" data-latex="{y} = -3 \, e^{\left(-2 \, t^{2} + 2 \, t + 2\right)}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-7742" title="F2 | Separation of variables | ver. 7742"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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} \cos\left(t\right) - 2 \, {y'} = 0 \hspace{2em} y( 0 )= 4" alt="2 \, {y} \cos\left(t\right) - 2 \, {y'} = 0 \hspace{2em} y( 0 )= 4" title="2 \, {y} \cos\left(t\right) - 2 \, {y'} = 0 \hspace{2em} y( 0 )= 4" data-latex="2 \, {y} \cos\left(t\right) - 2 \, {y'} = 0 \hspace{2em} y( 0 )= 4"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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%5Ccos%5Cleft(t%5Cright)%20-%202%20%5C,%20%7By'%7D%20=%200%20%5Chspace%7B2em%7D%20y(%200%20)=%204" alt="2 \, {y} \cos\left(t\right) - 2 \, {y'} = 0 \hspace{2em} y( 0 )= 4" title="2 \, {y} \cos\left(t\right) - 2 \, {y'} = 0 \hspace{2em} y( 0 )= 4" data-latex="2 \, {y} \cos\left(t\right) - 2 \, {y'} = 0 \hspace{2em} y( 0 )= 4"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y} = 4 \, e^{\sin\left(t\right)}" alt="{y} = 4 \, e^{\sin\left(t\right)}" title="{y} = 4 \, e^{\sin\left(t\right)}" data-latex="{y} = 4 \, e^{\sin\left(t\right)}"/></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,%20e%5E%7B%5Csin%5Cleft(t%5Cright)%7D" alt="{y} = 4 \, e^{\sin\left(t\right)}" title="{y} = 4 \, e^{\sin\left(t\right)}" data-latex="{y} = 4 \, e^{\sin\left(t\right)}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-8980" title="F2 | Separation of variables | ver. 8980"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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 - 6 \, {y} = 0 \hspace{2em} y( -1 )= 3" alt="2 \, {y'} t - 6 \, {y} = 0 \hspace{2em} y( -1 )= 3" title="2 \, {y'} t - 6 \, {y} = 0 \hspace{2em} y( -1 )= 3" data-latex="2 \, {y'} t - 6 \, {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;F2.&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%20t%20-%206%20%5C,%20%7By%7D%20=%200%20%5Chspace%7B2em%7D%20y(%20-1%20)=%203" alt="2 \, {y'} t - 6 \, {y} = 0 \hspace{2em} y( -1 )= 3" title="2 \, {y'} t - 6 \, {y} = 0 \hspace{2em} y( -1 )= 3" data-latex="2 \, {y'} t - 6 \, {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} = -3 \, t^{3}" alt="{y} = -3 \, t^{3}" title="{y} = -3 \, t^{3}" data-latex="{y} = -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=%20-3%20%5C,%20t%5E%7B3%7D" alt="{y} = -3 \, t^{3}" title="{y} = -3 \, t^{3}" data-latex="{y} = -3 \, t^{3}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-0556" title="F2 | Separation of variables | ver. 0556"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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 = 2 \, {y} {y'} - \frac{12 \, t}{{y}^{2}} - \frac{6}{{y}^{2}} \hspace{2em} y( -3 )= 3" alt="0 = 2 \, {y} {y'} - \frac{12 \, t}{{y}^{2}} - \frac{6}{{y}^{2}} \hspace{2em} y( -3 )= 3" title="0 = 2 \, {y} {y'} - \frac{12 \, t}{{y}^{2}} - \frac{6}{{y}^{2}} \hspace{2em} y( -3 )= 3" data-latex="0 = 2 \, {y} {y'} - \frac{12 \, t}{{y}^{2}} - \frac{6}{{y}^{2}} \hspace{2em} y( -3 )= 3"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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=%202%20%5C,%20%7By%7D%20%7By'%7D%20-%20%5Cfrac%7B12%20%5C,%20t%7D%7B%7By%7D%5E%7B2%7D%7D%20-%20%5Cfrac%7B6%7D%7B%7By%7D%5E%7B2%7D%7D%20%5Chspace%7B2em%7D%20y(%20-3%20)=%203" alt="0 = 2 \, {y} {y'} - \frac{12 \, t}{{y}^{2}} - \frac{6}{{y}^{2}} \hspace{2em} y( -3 )= 3" title="0 = 2 \, {y} {y'} - \frac{12 \, t}{{y}^{2}} - \frac{6}{{y}^{2}} \hspace{2em} y( -3 )= 3" data-latex="0 = 2 \, {y} {y'} - \frac{12 \, t}{{y}^{2}} - \frac{6}{{y}^{2}} \hspace{2em} y( -3 )= 3"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y} = {\left(3 \, t^{2} + 3 \, t + 9\right)}^{\frac{1}{3}}" alt="{y} = {\left(3 \, t^{2} + 3 \, t + 9\right)}^{\frac{1}{3}}" title="{y} = {\left(3 \, t^{2} + 3 \, t + 9\right)}^{\frac{1}{3}}" data-latex="{y} = {\left(3 \, t^{2} + 3 \, t + 9\right)}^{\frac{1}{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%7B%5Cleft(3%20%5C,%20t%5E%7B2%7D%20+%203%20%5C,%20t%20+%209%5Cright)%7D%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D" alt="{y} = {\left(3 \, t^{2} + 3 \, t + 9\right)}^{\frac{1}{3}}" title="{y} = {\left(3 \, t^{2} + 3 \, t + 9\right)}^{\frac{1}{3}}" data-latex="{y} = {\left(3 \, t^{2} + 3 \, t + 9\right)}^{\frac{1}{3}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-1021" title="F2 | Separation of variables | ver. 1021"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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'} = -4 \, {y} \sin\left(t\right) \hspace{2em} y( 0 )= 3 \, e^{\left(-2\right)}" alt="-2 \, {y'} = -4 \, {y} \sin\left(t\right) \hspace{2em} y( 0 )= 3 \, e^{\left(-2\right)}" title="-2 \, {y'} = -4 \, {y} \sin\left(t\right) \hspace{2em} y( 0 )= 3 \, e^{\left(-2\right)}" data-latex="-2 \, {y'} = -4 \, {y} \sin\left(t\right) \hspace{2em} y( 0 )= 3 \, e^{\left(-2\right)}"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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=%20-4%20%5C,%20%7By%7D%20%5Csin%5Cleft(t%5Cright)%20%5Chspace%7B2em%7D%20y(%200%20)=%203%20%5C,%20e%5E%7B%5Cleft(-2%5Cright)%7D" alt="-2 \, {y'} = -4 \, {y} \sin\left(t\right) \hspace{2em} y( 0 )= 3 \, e^{\left(-2\right)}" title="-2 \, {y'} = -4 \, {y} \sin\left(t\right) \hspace{2em} y( 0 )= 3 \, e^{\left(-2\right)}" data-latex="-2 \, {y'} = -4 \, {y} \sin\left(t\right) \hspace{2em} y( 0 )= 3 \, e^{\left(-2\right)}"&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 \, e^{\left(-2 \, \cos\left(t\right)\right)}" alt="{y} = 3 \, e^{\left(-2 \, \cos\left(t\right)\right)}" title="{y} = 3 \, e^{\left(-2 \, \cos\left(t\right)\right)}" data-latex="{y} = 3 \, e^{\left(-2 \, \cos\left(t\right)\right)}"/></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,%20e%5E%7B%5Cleft(-2%20%5C,%20%5Ccos%5Cleft(t%5Cright)%5Cright)%7D" alt="{y} = 3 \, e^{\left(-2 \, \cos\left(t\right)\right)}" title="{y} = 3 \, e^{\left(-2 \, \cos\left(t\right)\right)}" data-latex="{y} = 3 \, e^{\left(-2 \, \cos\left(t\right)\right)}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-5248" title="F2 | Separation of variables | ver. 5248"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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} {y'} = -\frac{12 \, t}{{y}} - \frac{6}{{y}} \hspace{2em} y( 3 )= 3" alt="-2 \, {y} {y'} = -\frac{12 \, t}{{y}} - \frac{6}{{y}} \hspace{2em} y( 3 )= 3" title="-2 \, {y} {y'} = -\frac{12 \, t}{{y}} - \frac{6}{{y}} \hspace{2em} y( 3 )= 3" data-latex="-2 \, {y} {y'} = -\frac{12 \, t}{{y}} - \frac{6}{{y}} \hspace{2em} y( 3 )= 3"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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%7By'%7D%20=%20-%5Cfrac%7B12%20%5C,%20t%7D%7B%7By%7D%7D%20-%20%5Cfrac%7B6%7D%7B%7By%7D%7D%20%5Chspace%7B2em%7D%20y(%203%20)=%203" alt="-2 \, {y} {y'} = -\frac{12 \, t}{{y}} - \frac{6}{{y}} \hspace{2em} y( 3 )= 3" title="-2 \, {y} {y'} = -\frac{12 \, t}{{y}} - \frac{6}{{y}} \hspace{2em} y( 3 )= 3" data-latex="-2 \, {y} {y'} = -\frac{12 \, t}{{y}} - \frac{6}{{y}} \hspace{2em} y( 3 )= 3"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y} = \sqrt{3 \, t^{2} + 3 \, t - 27}" alt="{y} = \sqrt{3 \, t^{2} + 3 \, t - 27}" title="{y} = \sqrt{3 \, t^{2} + 3 \, t - 27}" data-latex="{y} = \sqrt{3 \, t^{2} + 3 \, t - 27}"/></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%5Csqrt%7B3%20%5C,%20t%5E%7B2%7D%20+%203%20%5C,%20t%20-%2027%7D" alt="{y} = \sqrt{3 \, t^{2} + 3 \, t - 27}" title="{y} = \sqrt{3 \, t^{2} + 3 \, t - 27}" data-latex="{y} = \sqrt{3 \, t^{2} + 3 \, t - 27}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-1333" title="F2 | Separation of variables | ver. 1333"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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?-9 \, {y} \cos\left(t\right) = 3 \, {y'} \hspace{2em} y( 0 )= 4" alt="-9 \, {y} \cos\left(t\right) = 3 \, {y'} \hspace{2em} y( 0 )= 4" title="-9 \, {y} \cos\left(t\right) = 3 \, {y'} \hspace{2em} y( 0 )= 4" data-latex="-9 \, {y} \cos\left(t\right) = 3 \, {y'} \hspace{2em} y( 0 )= 4"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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?-9%20%5C,%20%7By%7D%20%5Ccos%5Cleft(t%5Cright)%20=%203%20%5C,%20%7By'%7D%20%5Chspace%7B2em%7D%20y(%200%20)=%204" alt="-9 \, {y} \cos\left(t\right) = 3 \, {y'} \hspace{2em} y( 0 )= 4" title="-9 \, {y} \cos\left(t\right) = 3 \, {y'} \hspace{2em} y( 0 )= 4" data-latex="-9 \, {y} \cos\left(t\right) = 3 \, {y'} \hspace{2em} y( 0 )= 4"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y} = 4 \, e^{\left(-3 \, \sin\left(t\right)\right)}" alt="{y} = 4 \, e^{\left(-3 \, \sin\left(t\right)\right)}" title="{y} = 4 \, e^{\left(-3 \, \sin\left(t\right)\right)}" data-latex="{y} = 4 \, e^{\left(-3 \, \sin\left(t\right)\right)}"/></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,%20e%5E%7B%5Cleft(-3%20%5C,%20%5Csin%5Cleft(t%5Cright)%5Cright)%7D" alt="{y} = 4 \, e^{\left(-3 \, \sin\left(t\right)\right)}" title="{y} = 4 \, e^{\left(-3 \, \sin\left(t\right)\right)}" data-latex="{y} = 4 \, e^{\left(-3 \, \sin\left(t\right)\right)}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-1912" title="F2 | Separation of variables | ver. 1912"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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{4 \, t}{{y}^{2}} - \frac{2}{{y}^{2}} = -2 \, {y'} {y} \hspace{2em} y( 2 )= 2" alt="-\frac{4 \, t}{{y}^{2}} - \frac{2}{{y}^{2}} = -2 \, {y'} {y} \hspace{2em} y( 2 )= 2" title="-\frac{4 \, t}{{y}^{2}} - \frac{2}{{y}^{2}} = -2 \, {y'} {y} \hspace{2em} y( 2 )= 2" data-latex="-\frac{4 \, t}{{y}^{2}} - \frac{2}{{y}^{2}} = -2 \, {y'} {y} \hspace{2em} y( 2 )= 2"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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%7B4%20%5C,%20t%7D%7B%7By%7D%5E%7B2%7D%7D%20-%20%5Cfrac%7B2%7D%7B%7By%7D%5E%7B2%7D%7D%20=%20-2%20%5C,%20%7By'%7D%20%7By%7D%20%5Chspace%7B2em%7D%20y(%202%20)=%202" alt="-\frac{4 \, t}{{y}^{2}} - \frac{2}{{y}^{2}} = -2 \, {y'} {y} \hspace{2em} y( 2 )= 2" title="-\frac{4 \, t}{{y}^{2}} - \frac{2}{{y}^{2}} = -2 \, {y'} {y} \hspace{2em} y( 2 )= 2" data-latex="-\frac{4 \, t}{{y}^{2}} - \frac{2}{{y}^{2}} = -2 \, {y'} {y} \hspace{2em} y( 2 )= 2"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y} = {\left(t^{2} + t + 2\right)}^{\frac{1}{3}}" alt="{y} = {\left(t^{2} + t + 2\right)}^{\frac{1}{3}}" title="{y} = {\left(t^{2} + t + 2\right)}^{\frac{1}{3}}" data-latex="{y} = {\left(t^{2} + t + 2\right)}^{\frac{1}{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%7B%5Cleft(t%5E%7B2%7D%20+%20t%20+%202%5Cright)%7D%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D" alt="{y} = {\left(t^{2} + t + 2\right)}^{\frac{1}{3}}" title="{y} = {\left(t^{2} + t + 2\right)}^{\frac{1}{3}}" data-latex="{y} = {\left(t^{2} + t + 2\right)}^{\frac{1}{3}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-7819" title="F2 | Separation of variables | ver. 7819"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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 = 6 \, {y} \cos\left(t\right) + 3 \, {y'} \hspace{2em} y( 0 )= 4" alt="0 = 6 \, {y} \cos\left(t\right) + 3 \, {y'} \hspace{2em} y( 0 )= 4" title="0 = 6 \, {y} \cos\left(t\right) + 3 \, {y'} \hspace{2em} y( 0 )= 4" data-latex="0 = 6 \, {y} \cos\left(t\right) + 3 \, {y'} \hspace{2em} y( 0 )= 4"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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=%206%20%5C,%20%7By%7D%20%5Ccos%5Cleft(t%5Cright)%20+%203%20%5C,%20%7By'%7D%20%5Chspace%7B2em%7D%20y(%200%20)=%204" alt="0 = 6 \, {y} \cos\left(t\right) + 3 \, {y'} \hspace{2em} y( 0 )= 4" title="0 = 6 \, {y} \cos\left(t\right) + 3 \, {y'} \hspace{2em} y( 0 )= 4" data-latex="0 = 6 \, {y} \cos\left(t\right) + 3 \, {y'} \hspace{2em} y( 0 )= 4"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y} = 4 \, e^{\left(-2 \, \sin\left(t\right)\right)}" alt="{y} = 4 \, e^{\left(-2 \, \sin\left(t\right)\right)}" title="{y} = 4 \, e^{\left(-2 \, \sin\left(t\right)\right)}" data-latex="{y} = 4 \, e^{\left(-2 \, \sin\left(t\right)\right)}"/></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,%20e%5E%7B%5Cleft(-2%20%5C,%20%5Csin%5Cleft(t%5Cright)%5Cright)%7D" alt="{y} = 4 \, e^{\left(-2 \, \sin\left(t\right)\right)}" title="{y} = 4 \, e^{\left(-2 \, \sin\left(t\right)\right)}" data-latex="{y} = 4 \, e^{\left(-2 \, \sin\left(t\right)\right)}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-5915" title="F2 | Separation of variables | ver. 5915"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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 - 6 \, {y} = 0 \hspace{2em} y( 1 )= -2" alt="2 \, {y'} t - 6 \, {y} = 0 \hspace{2em} y( 1 )= -2" title="2 \, {y'} t - 6 \, {y} = 0 \hspace{2em} y( 1 )= -2" data-latex="2 \, {y'} t - 6 \, {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;F2.&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%20t%20-%206%20%5C,%20%7By%7D%20=%200%20%5Chspace%7B2em%7D%20y(%201%20)=%20-2" alt="2 \, {y'} t - 6 \, {y} = 0 \hspace{2em} y( 1 )= -2" title="2 \, {y'} t - 6 \, {y} = 0 \hspace{2em} y( 1 )= -2" data-latex="2 \, {y'} t - 6 \, {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} = -2 \, t^{3}" alt="{y} = -2 \, t^{3}" title="{y} = -2 \, t^{3}" data-latex="{y} = -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=%20-2%20%5C,%20t%5E%7B3%7D" alt="{y} = -2 \, t^{3}" title="{y} = -2 \, t^{3}" data-latex="{y} = -2 \, t^{3}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-4172" title="F2 | Separation of variables | ver. 4172"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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 = -2 \, t {y'} - 6 \, {y} \hspace{2em} y( -2 )= -\frac{1}{4}" alt="0 = -2 \, t {y'} - 6 \, {y} \hspace{2em} y( -2 )= -\frac{1}{4}" title="0 = -2 \, t {y'} - 6 \, {y} \hspace{2em} y( -2 )= -\frac{1}{4}" data-latex="0 = -2 \, t {y'} - 6 \, {y} \hspace{2em} y( -2 )= -\frac{1}{4}"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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=%20-2%20%5C,%20t%20%7By'%7D%20-%206%20%5C,%20%7By%7D%20%5Chspace%7B2em%7D%20y(%20-2%20)=%20-%5Cfrac%7B1%7D%7B4%7D" alt="0 = -2 \, t {y'} - 6 \, {y} \hspace{2em} y( -2 )= -\frac{1}{4}" title="0 = -2 \, t {y'} - 6 \, {y} \hspace{2em} y( -2 )= -\frac{1}{4}" data-latex="0 = -2 \, t {y'} - 6 \, {y} \hspace{2em} y( -2 )= -\frac{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{2}{t^{3}}" alt="{y} = \frac{2}{t^{3}}" title="{y} = \frac{2}{t^{3}}" data-latex="{y} = \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%7B2%7D%7Bt%5E%7B3%7D%7D" alt="{y} = \frac{2}{t^{3}}" title="{y} = \frac{2}{t^{3}}" data-latex="{y} = \frac{2}{t^{3}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-1916" title="F2 | Separation of variables | ver. 1916"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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 = -4 \, {y} \hspace{2em} y( -3 )= -\frac{1}{9}" alt="2 \, {y'} t = -4 \, {y} \hspace{2em} y( -3 )= -\frac{1}{9}" title="2 \, {y'} t = -4 \, {y} \hspace{2em} y( -3 )= -\frac{1}{9}" data-latex="2 \, {y'} t = -4 \, {y} \hspace{2em} y( -3 )= -\frac{1}{9}"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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%20t%20=%20-4%20%5C,%20%7By%7D%20%5Chspace%7B2em%7D%20y(%20-3%20)=%20-%5Cfrac%7B1%7D%7B9%7D" alt="2 \, {y'} t = -4 \, {y} \hspace{2em} y( -3 )= -\frac{1}{9}" title="2 \, {y'} t = -4 \, {y} \hspace{2em} y( -3 )= -\frac{1}{9}" data-latex="2 \, {y'} t = -4 \, {y} \hspace{2em} y( -3 )= -\frac{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} = -\frac{1}{t^{2}}" alt="{y} = -\frac{1}{t^{2}}" title="{y} = -\frac{1}{t^{2}}" data-latex="{y} = -\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%7B1%7D%7Bt%5E%7B2%7D%7D" alt="{y} = -\frac{1}{t^{2}}" title="{y} = -\frac{1}{t^{2}}" data-latex="{y} = -\frac{1}{t^{2}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-9342" title="F2 | Separation of variables | ver. 9342"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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'} t - 6 \, {y} = 0 \hspace{2em} y( -4 )= -16" alt="3 \, {y'} t - 6 \, {y} = 0 \hspace{2em} y( -4 )= -16" title="3 \, {y'} t - 6 \, {y} = 0 \hspace{2em} y( -4 )= -16" data-latex="3 \, {y'} t - 6 \, {y} = 0 \hspace{2em} y( -4 )= -16"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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%20t%20-%206%20%5C,%20%7By%7D%20=%200%20%5Chspace%7B2em%7D%20y(%20-4%20)=%20-16" alt="3 \, {y'} t - 6 \, {y} = 0 \hspace{2em} y( -4 )= -16" title="3 \, {y'} t - 6 \, {y} = 0 \hspace{2em} y( -4 )= -16" data-latex="3 \, {y'} t - 6 \, {y} = 0 \hspace{2em} y( -4 )= -16"&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}" alt="{y} = -t^{2}" title="{y} = -t^{2}" data-latex="{y} = -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" alt="{y} = -t^{2}" title="{y} = -t^{2}" data-latex="{y} = -t^{2}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-7496" title="F2 | Separation of variables | ver. 7496"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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 = -3 \, {y} \cos\left(t\right) - 3 \, {y'} \hspace{2em} y( 0 )= -1" alt="0 = -3 \, {y} \cos\left(t\right) - 3 \, {y'} \hspace{2em} y( 0 )= -1" title="0 = -3 \, {y} \cos\left(t\right) - 3 \, {y'} \hspace{2em} y( 0 )= -1" data-latex="0 = -3 \, {y} \cos\left(t\right) - 3 \, {y'} \hspace{2em} y( 0 )= -1"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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=%20-3%20%5C,%20%7By%7D%20%5Ccos%5Cleft(t%5Cright)%20-%203%20%5C,%20%7By'%7D%20%5Chspace%7B2em%7D%20y(%200%20)=%20-1" alt="0 = -3 \, {y} \cos\left(t\right) - 3 \, {y'} \hspace{2em} y( 0 )= -1" title="0 = -3 \, {y} \cos\left(t\right) - 3 \, {y'} \hspace{2em} y( 0 )= -1" data-latex="0 = -3 \, {y} \cos\left(t\right) - 3 \, {y'} \hspace{2em} y( 0 )= -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} = -e^{\left(-\sin\left(t\right)\right)}" alt="{y} = -e^{\left(-\sin\left(t\right)\right)}" title="{y} = -e^{\left(-\sin\left(t\right)\right)}" data-latex="{y} = -e^{\left(-\sin\left(t\right)\right)}"/></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-e%5E%7B%5Cleft(-%5Csin%5Cleft(t%5Cright)%5Cright)%7D" alt="{y} = -e^{\left(-\sin\left(t\right)\right)}" title="{y} = -e^{\left(-\sin\left(t\right)\right)}" data-latex="{y} = -e^{\left(-\sin\left(t\right)\right)}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-0923" title="F2 | Separation of variables | ver. 0923"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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'} = -3 \, {y} {\left(2 \, t - 3\right)} \hspace{2em} y( 0 )= 2 \, e^{\left(-4\right)}" alt="-3 \, {y'} = -3 \, {y} {\left(2 \, t - 3\right)} \hspace{2em} y( 0 )= 2 \, e^{\left(-4\right)}" title="-3 \, {y'} = -3 \, {y} {\left(2 \, t - 3\right)} \hspace{2em} y( 0 )= 2 \, e^{\left(-4\right)}" data-latex="-3 \, {y'} = -3 \, {y} {\left(2 \, t - 3\right)} \hspace{2em} y( 0 )= 2 \, e^{\left(-4\right)}"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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=%20-3%20%5C,%20%7By%7D%20%7B%5Cleft(2%20%5C,%20t%20-%203%5Cright)%7D%20%5Chspace%7B2em%7D%20y(%200%20)=%202%20%5C,%20e%5E%7B%5Cleft(-4%5Cright)%7D" alt="-3 \, {y'} = -3 \, {y} {\left(2 \, t - 3\right)} \hspace{2em} y( 0 )= 2 \, e^{\left(-4\right)}" title="-3 \, {y'} = -3 \, {y} {\left(2 \, t - 3\right)} \hspace{2em} y( 0 )= 2 \, e^{\left(-4\right)}" data-latex="-3 \, {y'} = -3 \, {y} {\left(2 \, t - 3\right)} \hspace{2em} y( 0 )= 2 \, e^{\left(-4\right)}"&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 \, e^{\left(t^{2} - 3 \, t - 4\right)}" alt="{y} = 2 \, e^{\left(t^{2} - 3 \, t - 4\right)}" title="{y} = 2 \, e^{\left(t^{2} - 3 \, t - 4\right)}" data-latex="{y} = 2 \, e^{\left(t^{2} - 3 \, t - 4\right)}"/></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,%20e%5E%7B%5Cleft(t%5E%7B2%7D%20-%203%20%5C,%20t%20-%204%5Cright)%7D" alt="{y} = 2 \, e^{\left(t^{2} - 3 \, t - 4\right)}" title="{y} = 2 \, e^{\left(t^{2} - 3 \, t - 4\right)}" data-latex="{y} = 2 \, e^{\left(t^{2} - 3 \, t - 4\right)}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-1891" title="F2 | Separation of variables | ver. 1891"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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}^{2} {y'} - \frac{6}{{y}} = \frac{4 \, t}{{y}} \hspace{2em} y( -3 )= 2" alt="2 \, {y}^{2} {y'} - \frac{6}{{y}} = \frac{4 \, t}{{y}} \hspace{2em} y( -3 )= 2" title="2 \, {y}^{2} {y'} - \frac{6}{{y}} = \frac{4 \, t}{{y}} \hspace{2em} y( -3 )= 2" data-latex="2 \, {y}^{2} {y'} - \frac{6}{{y}} = \frac{4 \, t}{{y}} \hspace{2em} y( -3 )= 2"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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%5E%7B2%7D%20%7By'%7D%20-%20%5Cfrac%7B6%7D%7B%7By%7D%7D%20=%20%5Cfrac%7B4%20%5C,%20t%7D%7B%7By%7D%7D%20%5Chspace%7B2em%7D%20y(%20-3%20)=%202" alt="2 \, {y}^{2} {y'} - \frac{6}{{y}} = \frac{4 \, t}{{y}} \hspace{2em} y( -3 )= 2" title="2 \, {y}^{2} {y'} - \frac{6}{{y}} = \frac{4 \, t}{{y}} \hspace{2em} y( -3 )= 2" data-latex="2 \, {y}^{2} {y'} - \frac{6}{{y}} = \frac{4 \, t}{{y}} \hspace{2em} y( -3 )= 2"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y} = {\left(t^{2} + 3 \, t + 8\right)}^{\frac{1}{3}}" alt="{y} = {\left(t^{2} + 3 \, t + 8\right)}^{\frac{1}{3}}" title="{y} = {\left(t^{2} + 3 \, t + 8\right)}^{\frac{1}{3}}" data-latex="{y} = {\left(t^{2} + 3 \, t + 8\right)}^{\frac{1}{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%7B%5Cleft(t%5E%7B2%7D%20+%203%20%5C,%20t%20+%208%5Cright)%7D%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D" alt="{y} = {\left(t^{2} + 3 \, t + 8\right)}^{\frac{1}{3}}" title="{y} = {\left(t^{2} + 3 \, t + 8\right)}^{\frac{1}{3}}" data-latex="{y} = {\left(t^{2} + 3 \, t + 8\right)}^{\frac{1}{3}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-2883" title="F2 | Separation of variables | ver. 2883"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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} {y'} - \frac{12 \, t}{{y}} = \frac{4}{{y}} \hspace{2em} y( -2 )= 3" alt="2 \, {y} {y'} - \frac{12 \, t}{{y}} = \frac{4}{{y}} \hspace{2em} y( -2 )= 3" title="2 \, {y} {y'} - \frac{12 \, t}{{y}} = \frac{4}{{y}} \hspace{2em} y( -2 )= 3" data-latex="2 \, {y} {y'} - \frac{12 \, t}{{y}} = \frac{4}{{y}} \hspace{2em} y( -2 )= 3"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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%7By'%7D%20-%20%5Cfrac%7B12%20%5C,%20t%7D%7B%7By%7D%7D%20=%20%5Cfrac%7B4%7D%7B%7By%7D%7D%20%5Chspace%7B2em%7D%20y(%20-2%20)=%203" alt="2 \, {y} {y'} - \frac{12 \, t}{{y}} = \frac{4}{{y}} \hspace{2em} y( -2 )= 3" title="2 \, {y} {y'} - \frac{12 \, t}{{y}} = \frac{4}{{y}} \hspace{2em} y( -2 )= 3" data-latex="2 \, {y} {y'} - \frac{12 \, t}{{y}} = \frac{4}{{y}} \hspace{2em} y( -2 )= 3"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y} = \sqrt{3 \, t^{2} + 2 \, t + 1}" alt="{y} = \sqrt{3 \, t^{2} + 2 \, t + 1}" title="{y} = \sqrt{3 \, t^{2} + 2 \, t + 1}" data-latex="{y} = \sqrt{3 \, t^{2} + 2 \, t + 1}"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%7By%7D%20=%20%5Csqrt%7B3%20%5C,%20t%5E%7B2%7D%20+%202%20%5C,%20t%20+%201%7D" alt="{y} = \sqrt{3 \, t^{2} + 2 \, t + 1}" title="{y} = \sqrt{3 \, t^{2} + 2 \, t + 1}" data-latex="{y} = \sqrt{3 \, t^{2} + 2 \, t + 1}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-0735" title="F2 | Separation of variables | ver. 0735"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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 \, t {y'} = -9 \, {y} \hspace{2em} y( 4 )= \frac{3}{64}" alt="3 \, t {y'} = -9 \, {y} \hspace{2em} y( 4 )= \frac{3}{64}" title="3 \, t {y'} = -9 \, {y} \hspace{2em} y( 4 )= \frac{3}{64}" data-latex="3 \, t {y'} = -9 \, {y} \hspace{2em} y( 4 )= \frac{3}{64}"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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,%20t%20%7By'%7D%20=%20-9%20%5C,%20%7By%7D%20%5Chspace%7B2em%7D%20y(%204%20)=%20%5Cfrac%7B3%7D%7B64%7D" alt="3 \, t {y'} = -9 \, {y} \hspace{2em} y( 4 )= \frac{3}{64}" title="3 \, t {y'} = -9 \, {y} \hspace{2em} y( 4 )= \frac{3}{64}" data-latex="3 \, t {y'} = -9 \, {y} \hspace{2em} y( 4 )= \frac{3}{64}"&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}}" alt="{y} = \frac{3}{t^{3}}" title="{y} = \frac{3}{t^{3}}" data-latex="{y} = \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%7B3%7D%7Bt%5E%7B3%7D%7D" alt="{y} = \frac{3}{t^{3}}" title="{y} = \frac{3}{t^{3}}" data-latex="{y} = \frac{3}{t^{3}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-4099" title="F2 | Separation of variables | ver. 4099"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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'} = 2 \, {y} {\left(2 \, t - 1\right)} \hspace{2em} y( 0 )= -e^{4}" alt="-2 \, {y'} = 2 \, {y} {\left(2 \, t - 1\right)} \hspace{2em} y( 0 )= -e^{4}" title="-2 \, {y'} = 2 \, {y} {\left(2 \, t - 1\right)} \hspace{2em} y( 0 )= -e^{4}" data-latex="-2 \, {y'} = 2 \, {y} {\left(2 \, t - 1\right)} \hspace{2em} y( 0 )= -e^{4}"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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=%202%20%5C,%20%7By%7D%20%7B%5Cleft(2%20%5C,%20t%20-%201%5Cright)%7D%20%5Chspace%7B2em%7D%20y(%200%20)=%20-e%5E%7B4%7D" alt="-2 \, {y'} = 2 \, {y} {\left(2 \, t - 1\right)} \hspace{2em} y( 0 )= -e^{4}" title="-2 \, {y'} = 2 \, {y} {\left(2 \, t - 1\right)} \hspace{2em} y( 0 )= -e^{4}" data-latex="-2 \, {y'} = 2 \, {y} {\left(2 \, t - 1\right)} \hspace{2em} y( 0 )= -e^{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} = -e^{\left(-t^{2} + t + 4\right)}" alt="{y} = -e^{\left(-t^{2} + t + 4\right)}" title="{y} = -e^{\left(-t^{2} + t + 4\right)}" data-latex="{y} = -e^{\left(-t^{2} + t + 4\right)}"/></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-e%5E%7B%5Cleft(-t%5E%7B2%7D%20+%20t%20+%204%5Cright)%7D" alt="{y} = -e^{\left(-t^{2} + t + 4\right)}" title="{y} = -e^{\left(-t^{2} + t + 4\right)}" data-latex="{y} = -e^{\left(-t^{2} + t + 4\right)}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-0635" title="F2 | Separation of variables | ver. 0635"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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 = -3 \, {y'} t + 9 \, {y} \hspace{2em} y( -2 )= -32" alt="0 = -3 \, {y'} t + 9 \, {y} \hspace{2em} y( -2 )= -32" title="0 = -3 \, {y'} t + 9 \, {y} \hspace{2em} y( -2 )= -32" data-latex="0 = -3 \, {y'} t + 9 \, {y} \hspace{2em} y( -2 )= -32"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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=%20-3%20%5C,%20%7By'%7D%20t%20+%209%20%5C,%20%7By%7D%20%5Chspace%7B2em%7D%20y(%20-2%20)=%20-32" alt="0 = -3 \, {y'} t + 9 \, {y} \hspace{2em} y( -2 )= -32" title="0 = -3 \, {y'} t + 9 \, {y} \hspace{2em} y( -2 )= -32" data-latex="0 = -3 \, {y'} t + 9 \, {y} \hspace{2em} y( -2 )= -32"&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}" alt="{y} = 4 \, t^{3}" title="{y} = 4 \, t^{3}" data-latex="{y} = 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=%204%20%5C,%20t%5E%7B3%7D" alt="{y} = 4 \, t^{3}" title="{y} = 4 \, t^{3}" data-latex="{y} = 4 \, t^{3}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-4082" title="F2 | Separation of variables | ver. 4082"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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 = 2 \, {y} \cos\left(t\right) - 2 \, {y'} \hspace{2em} y( 0 )= -2" alt="0 = 2 \, {y} \cos\left(t\right) - 2 \, {y'} \hspace{2em} y( 0 )= -2" title="0 = 2 \, {y} \cos\left(t\right) - 2 \, {y'} \hspace{2em} y( 0 )= -2" data-latex="0 = 2 \, {y} \cos\left(t\right) - 2 \, {y'} \hspace{2em} y( 0 )= -2"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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=%202%20%5C,%20%7By%7D%20%5Ccos%5Cleft(t%5Cright)%20-%202%20%5C,%20%7By'%7D%20%5Chspace%7B2em%7D%20y(%200%20)=%20-2" alt="0 = 2 \, {y} \cos\left(t\right) - 2 \, {y'} \hspace{2em} y( 0 )= -2" title="0 = 2 \, {y} \cos\left(t\right) - 2 \, {y'} \hspace{2em} y( 0 )= -2" data-latex="0 = 2 \, {y} \cos\left(t\right) - 2 \, {y'} \hspace{2em} y( 0 )= -2"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y} = -2 \, e^{\sin\left(t\right)}" alt="{y} = -2 \, e^{\sin\left(t\right)}" title="{y} = -2 \, e^{\sin\left(t\right)}" data-latex="{y} = -2 \, e^{\sin\left(t\right)}"/></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,%20e%5E%7B%5Csin%5Cleft(t%5Cright)%7D" alt="{y} = -2 \, e^{\sin\left(t\right)}" title="{y} = -2 \, e^{\sin\left(t\right)}" data-latex="{y} = -2 \, e^{\sin\left(t\right)}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-4695" title="F2 | Separation of variables | ver. 4695"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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'} = \frac{18 \, t}{{y}^{2}} + \frac{9}{{y}^{2}} \hspace{2em} y( 3 )= 3" alt="3 \, {y} {y'} = \frac{18 \, t}{{y}^{2}} + \frac{9}{{y}^{2}} \hspace{2em} y( 3 )= 3" title="3 \, {y} {y'} = \frac{18 \, t}{{y}^{2}} + \frac{9}{{y}^{2}} \hspace{2em} y( 3 )= 3" data-latex="3 \, {y} {y'} = \frac{18 \, t}{{y}^{2}} + \frac{9}{{y}^{2}} \hspace{2em} y( 3 )= 3"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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%7By'%7D%20=%20%5Cfrac%7B18%20%5C,%20t%7D%7B%7By%7D%5E%7B2%7D%7D%20+%20%5Cfrac%7B9%7D%7B%7By%7D%5E%7B2%7D%7D%20%5Chspace%7B2em%7D%20y(%203%20)=%203" alt="3 \, {y} {y'} = \frac{18 \, t}{{y}^{2}} + \frac{9}{{y}^{2}} \hspace{2em} y( 3 )= 3" title="3 \, {y} {y'} = \frac{18 \, t}{{y}^{2}} + \frac{9}{{y}^{2}} \hspace{2em} y( 3 )= 3" data-latex="3 \, {y} {y'} = \frac{18 \, t}{{y}^{2}} + \frac{9}{{y}^{2}} \hspace{2em} y( 3 )= 3"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y} = {\left(3 \, t^{2} + 3 \, t - 9\right)}^{\frac{1}{3}}" alt="{y} = {\left(3 \, t^{2} + 3 \, t - 9\right)}^{\frac{1}{3}}" title="{y} = {\left(3 \, t^{2} + 3 \, t - 9\right)}^{\frac{1}{3}}" data-latex="{y} = {\left(3 \, t^{2} + 3 \, t - 9\right)}^{\frac{1}{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%7B%5Cleft(3%20%5C,%20t%5E%7B2%7D%20+%203%20%5C,%20t%20-%209%5Cright)%7D%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D" alt="{y} = {\left(3 \, t^{2} + 3 \, t - 9\right)}^{\frac{1}{3}}" title="{y} = {\left(3 \, t^{2} + 3 \, t - 9\right)}^{\frac{1}{3}}" data-latex="{y} = {\left(3 \, t^{2} + 3 \, t - 9\right)}^{\frac{1}{3}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-2328" title="F2 | Separation of variables | ver. 2328"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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} - \frac{12 \, t}{{y}} = \frac{3}{{y}} \hspace{2em} y( 3 )= 3" alt="3 \, {y'} {y} - \frac{12 \, t}{{y}} = \frac{3}{{y}} \hspace{2em} y( 3 )= 3" title="3 \, {y'} {y} - \frac{12 \, t}{{y}} = \frac{3}{{y}} \hspace{2em} y( 3 )= 3" data-latex="3 \, {y'} {y} - \frac{12 \, t}{{y}} = \frac{3}{{y}} \hspace{2em} y( 3 )= 3"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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%7By%7D%20-%20%5Cfrac%7B12%20%5C,%20t%7D%7B%7By%7D%7D%20=%20%5Cfrac%7B3%7D%7B%7By%7D%7D%20%5Chspace%7B2em%7D%20y(%203%20)=%203" alt="3 \, {y'} {y} - \frac{12 \, t}{{y}} = \frac{3}{{y}} \hspace{2em} y( 3 )= 3" title="3 \, {y'} {y} - \frac{12 \, t}{{y}} = \frac{3}{{y}} \hspace{2em} y( 3 )= 3" data-latex="3 \, {y'} {y} - \frac{12 \, t}{{y}} = \frac{3}{{y}} \hspace{2em} y( 3 )= 3"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y} = \sqrt{2 \, t^{2} + t - 12}" alt="{y} = \sqrt{2 \, t^{2} + t - 12}" title="{y} = \sqrt{2 \, t^{2} + t - 12}" data-latex="{y} = \sqrt{2 \, t^{2} + t - 12}"/></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%5Csqrt%7B2%20%5C,%20t%5E%7B2%7D%20+%20t%20-%2012%7D" alt="{y} = \sqrt{2 \, t^{2} + t - 12}" title="{y} = \sqrt{2 \, t^{2} + t - 12}" data-latex="{y} = \sqrt{2 \, t^{2} + t - 12}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-0513" title="F2 | Separation of variables | ver. 0513"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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}^{2} {y'} - \frac{9}{{y}} = \frac{12 \, t}{{y}} \hspace{2em} y( 3 )= 2" alt="3 \, {y}^{2} {y'} - \frac{9}{{y}} = \frac{12 \, t}{{y}} \hspace{2em} y( 3 )= 2" title="3 \, {y}^{2} {y'} - \frac{9}{{y}} = \frac{12 \, t}{{y}} \hspace{2em} y( 3 )= 2" data-latex="3 \, {y}^{2} {y'} - \frac{9}{{y}} = \frac{12 \, t}{{y}} \hspace{2em} y( 3 )= 2"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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%5E%7B2%7D%20%7By'%7D%20-%20%5Cfrac%7B9%7D%7B%7By%7D%7D%20=%20%5Cfrac%7B12%20%5C,%20t%7D%7B%7By%7D%7D%20%5Chspace%7B2em%7D%20y(%203%20)=%202" alt="3 \, {y}^{2} {y'} - \frac{9}{{y}} = \frac{12 \, t}{{y}} \hspace{2em} y( 3 )= 2" title="3 \, {y}^{2} {y'} - \frac{9}{{y}} = \frac{12 \, t}{{y}} \hspace{2em} y( 3 )= 2" data-latex="3 \, {y}^{2} {y'} - \frac{9}{{y}} = \frac{12 \, t}{{y}} \hspace{2em} y( 3 )= 2"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y} = {\left(2 \, t^{2} + 3 \, t - 19\right)}^{\frac{1}{3}}" alt="{y} = {\left(2 \, t^{2} + 3 \, t - 19\right)}^{\frac{1}{3}}" title="{y} = {\left(2 \, t^{2} + 3 \, t - 19\right)}^{\frac{1}{3}}" data-latex="{y} = {\left(2 \, t^{2} + 3 \, t - 19\right)}^{\frac{1}{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%7B%5Cleft(2%20%5C,%20t%5E%7B2%7D%20+%203%20%5C,%20t%20-%2019%5Cright)%7D%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D" alt="{y} = {\left(2 \, t^{2} + 3 \, t - 19\right)}^{\frac{1}{3}}" title="{y} = {\left(2 \, t^{2} + 3 \, t - 19\right)}^{\frac{1}{3}}" data-latex="{y} = {\left(2 \, t^{2} + 3 \, t - 19\right)}^{\frac{1}{3}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-6625" title="F2 | Separation of variables | ver. 6625"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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 {y'} = 4 \, {y} \hspace{2em} y( -4 )= \frac{1}{8}" alt="-2 \, t {y'} = 4 \, {y} \hspace{2em} y( -4 )= \frac{1}{8}" title="-2 \, t {y'} = 4 \, {y} \hspace{2em} y( -4 )= \frac{1}{8}" data-latex="-2 \, t {y'} = 4 \, {y} \hspace{2em} y( -4 )= \frac{1}{8}"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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%20%7By'%7D%20=%204%20%5C,%20%7By%7D%20%5Chspace%7B2em%7D%20y(%20-4%20)=%20%5Cfrac%7B1%7D%7B8%7D" alt="-2 \, t {y'} = 4 \, {y} \hspace{2em} y( -4 )= \frac{1}{8}" title="-2 \, t {y'} = 4 \, {y} \hspace{2em} y( -4 )= \frac{1}{8}" data-latex="-2 \, t {y'} = 4 \, {y} \hspace{2em} y( -4 )= \frac{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{2}{t^{2}}" alt="{y} = \frac{2}{t^{2}}" title="{y} = \frac{2}{t^{2}}" data-latex="{y} = \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%5Cfrac%7B2%7D%7Bt%5E%7B2%7D%7D" alt="{y} = \frac{2}{t^{2}}" title="{y} = \frac{2}{t^{2}}" data-latex="{y} = \frac{2}{t^{2}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-0624" title="F2 | Separation of variables | ver. 0624"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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}{{y}} = -2 \, {y} {y'} + \frac{12 \, t}{{y}} \hspace{2em} y( 2 )= 4" alt="-\frac{6}{{y}} = -2 \, {y} {y'} + \frac{12 \, t}{{y}} \hspace{2em} y( 2 )= 4" title="-\frac{6}{{y}} = -2 \, {y} {y'} + \frac{12 \, t}{{y}} \hspace{2em} y( 2 )= 4" data-latex="-\frac{6}{{y}} = -2 \, {y} {y'} + \frac{12 \, t}{{y}} \hspace{2em} y( 2 )= 4"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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%7B%7By%7D%7D%20=%20-2%20%5C,%20%7By%7D%20%7By'%7D%20+%20%5Cfrac%7B12%20%5C,%20t%7D%7B%7By%7D%7D%20%5Chspace%7B2em%7D%20y(%202%20)=%204" alt="-\frac{6}{{y}} = -2 \, {y} {y'} + \frac{12 \, t}{{y}} \hspace{2em} y( 2 )= 4" title="-\frac{6}{{y}} = -2 \, {y} {y'} + \frac{12 \, t}{{y}} \hspace{2em} y( 2 )= 4" data-latex="-\frac{6}{{y}} = -2 \, {y} {y'} + \frac{12 \, t}{{y}} \hspace{2em} y( 2 )= 4"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y} = \sqrt{3 \, t^{2} + 3 \, t - 2}" alt="{y} = \sqrt{3 \, t^{2} + 3 \, t - 2}" title="{y} = \sqrt{3 \, t^{2} + 3 \, t - 2}" data-latex="{y} = \sqrt{3 \, t^{2} + 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%5Csqrt%7B3%20%5C,%20t%5E%7B2%7D%20+%203%20%5C,%20t%20-%202%7D" alt="{y} = \sqrt{3 \, t^{2} + 3 \, t - 2}" title="{y} = \sqrt{3 \, t^{2} + 3 \, t - 2}" data-latex="{y} = \sqrt{3 \, t^{2} + 3 \, t - 2}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-3543" title="F2 | Separation of variables | ver. 3543"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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 \, {y} \sin\left(t\right) = 2 \, {y'} \hspace{2em} y( 0 )= 3 \, e^{\left(-3\right)}" alt="6 \, {y} \sin\left(t\right) = 2 \, {y'} \hspace{2em} y( 0 )= 3 \, e^{\left(-3\right)}" title="6 \, {y} \sin\left(t\right) = 2 \, {y'} \hspace{2em} y( 0 )= 3 \, e^{\left(-3\right)}" data-latex="6 \, {y} \sin\left(t\right) = 2 \, {y'} \hspace{2em} y( 0 )= 3 \, e^{\left(-3\right)}"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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,%20%7By%7D%20%5Csin%5Cleft(t%5Cright)%20=%202%20%5C,%20%7By'%7D%20%5Chspace%7B2em%7D%20y(%200%20)=%203%20%5C,%20e%5E%7B%5Cleft(-3%5Cright)%7D" alt="6 \, {y} \sin\left(t\right) = 2 \, {y'} \hspace{2em} y( 0 )= 3 \, e^{\left(-3\right)}" title="6 \, {y} \sin\left(t\right) = 2 \, {y'} \hspace{2em} y( 0 )= 3 \, e^{\left(-3\right)}" data-latex="6 \, {y} \sin\left(t\right) = 2 \, {y'} \hspace{2em} y( 0 )= 3 \, e^{\left(-3\right)}"&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 \, e^{\left(-3 \, \cos\left(t\right)\right)}" alt="{y} = 3 \, e^{\left(-3 \, \cos\left(t\right)\right)}" title="{y} = 3 \, e^{\left(-3 \, \cos\left(t\right)\right)}" data-latex="{y} = 3 \, e^{\left(-3 \, \cos\left(t\right)\right)}"/></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,%20e%5E%7B%5Cleft(-3%20%5C,%20%5Ccos%5Cleft(t%5Cright)%5Cright)%7D" alt="{y} = 3 \, e^{\left(-3 \, \cos\left(t\right)\right)}" title="{y} = 3 \, e^{\left(-3 \, \cos\left(t\right)\right)}" data-latex="{y} = 3 \, e^{\left(-3 \, \cos\left(t\right)\right)}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-8487" title="F2 | Separation of variables | ver. 8487"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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 = -4 \, {y} \cos\left(t\right) + 2 \, {y'} \hspace{2em} y( 0 )= -4" alt="0 = -4 \, {y} \cos\left(t\right) + 2 \, {y'} \hspace{2em} y( 0 )= -4" title="0 = -4 \, {y} \cos\left(t\right) + 2 \, {y'} \hspace{2em} y( 0 )= -4" data-latex="0 = -4 \, {y} \cos\left(t\right) + 2 \, {y'} \hspace{2em} y( 0 )= -4"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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=%20-4%20%5C,%20%7By%7D%20%5Ccos%5Cleft(t%5Cright)%20+%202%20%5C,%20%7By'%7D%20%5Chspace%7B2em%7D%20y(%200%20)=%20-4" alt="0 = -4 \, {y} \cos\left(t\right) + 2 \, {y'} \hspace{2em} y( 0 )= -4" title="0 = -4 \, {y} \cos\left(t\right) + 2 \, {y'} \hspace{2em} y( 0 )= -4" data-latex="0 = -4 \, {y} \cos\left(t\right) + 2 \, {y'} \hspace{2em} y( 0 )= -4"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y} = -4 \, e^{\left(2 \, \sin\left(t\right)\right)}" alt="{y} = -4 \, e^{\left(2 \, \sin\left(t\right)\right)}" title="{y} = -4 \, e^{\left(2 \, \sin\left(t\right)\right)}" data-latex="{y} = -4 \, e^{\left(2 \, \sin\left(t\right)\right)}"/></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,%20e%5E%7B%5Cleft(2%20%5C,%20%5Csin%5Cleft(t%5Cright)%5Cright)%7D" alt="{y} = -4 \, e^{\left(2 \, \sin\left(t\right)\right)}" title="{y} = -4 \, e^{\left(2 \, \sin\left(t\right)\right)}" data-latex="{y} = -4 \, e^{\left(2 \, \sin\left(t\right)\right)}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-5234" title="F2 | Separation of variables | ver. 5234"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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}{{y}} = 3 \, {y} {y'} - \frac{12 \, t}{{y}} \hspace{2em} y( -3 )= 2" alt="\frac{6}{{y}} = 3 \, {y} {y'} - \frac{12 \, t}{{y}} \hspace{2em} y( -3 )= 2" title="\frac{6}{{y}} = 3 \, {y} {y'} - \frac{12 \, t}{{y}} \hspace{2em} y( -3 )= 2" data-latex="\frac{6}{{y}} = 3 \, {y} {y'} - \frac{12 \, t}{{y}} \hspace{2em} y( -3 )= 2"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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%7B%7By%7D%7D%20=%203%20%5C,%20%7By%7D%20%7By'%7D%20-%20%5Cfrac%7B12%20%5C,%20t%7D%7B%7By%7D%7D%20%5Chspace%7B2em%7D%20y(%20-3%20)=%202" alt="\frac{6}{{y}} = 3 \, {y} {y'} - \frac{12 \, t}{{y}} \hspace{2em} y( -3 )= 2" title="\frac{6}{{y}} = 3 \, {y} {y'} - \frac{12 \, t}{{y}} \hspace{2em} y( -3 )= 2" data-latex="\frac{6}{{y}} = 3 \, {y} {y'} - \frac{12 \, t}{{y}} \hspace{2em} y( -3 )= 2"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y} = \sqrt{2 \, t^{2} + 2 \, t - 8}" alt="{y} = \sqrt{2 \, t^{2} + 2 \, t - 8}" title="{y} = \sqrt{2 \, t^{2} + 2 \, t - 8}" data-latex="{y} = \sqrt{2 \, t^{2} + 2 \, t - 8}"/></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%5Csqrt%7B2%20%5C,%20t%5E%7B2%7D%20+%202%20%5C,%20t%20-%208%7D" alt="{y} = \sqrt{2 \, t^{2} + 2 \, t - 8}" title="{y} = \sqrt{2 \, t^{2} + 2 \, t - 8}" data-latex="{y} = \sqrt{2 \, t^{2} + 2 \, t - 8}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-7731" title="F2 | Separation of variables | ver. 7731"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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'} = 8 \, {y} t \hspace{2em} y( 0 )= 2 \, e^{5}" alt="2 \, {y'} = 8 \, {y} t \hspace{2em} y( 0 )= 2 \, e^{5}" title="2 \, {y'} = 8 \, {y} t \hspace{2em} y( 0 )= 2 \, e^{5}" data-latex="2 \, {y'} = 8 \, {y} t \hspace{2em} y( 0 )= 2 \, e^{5}"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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=%208%20%5C,%20%7By%7D%20t%20%5Chspace%7B2em%7D%20y(%200%20)=%202%20%5C,%20e%5E%7B5%7D" alt="2 \, {y'} = 8 \, {y} t \hspace{2em} y( 0 )= 2 \, e^{5}" title="2 \, {y'} = 8 \, {y} t \hspace{2em} y( 0 )= 2 \, e^{5}" data-latex="2 \, {y'} = 8 \, {y} t \hspace{2em} y( 0 )= 2 \, e^{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} = 2 \, e^{\left(2 \, t^{2} + 5\right)}" alt="{y} = 2 \, e^{\left(2 \, t^{2} + 5\right)}" title="{y} = 2 \, e^{\left(2 \, t^{2} + 5\right)}" data-latex="{y} = 2 \, e^{\left(2 \, t^{2} + 5\right)}"/></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,%20e%5E%7B%5Cleft(2%20%5C,%20t%5E%7B2%7D%20+%205%5Cright)%7D" alt="{y} = 2 \, e^{\left(2 \, t^{2} + 5\right)}" title="{y} = 2 \, e^{\left(2 \, t^{2} + 5\right)}" data-latex="{y} = 2 \, e^{\left(2 \, t^{2} + 5\right)}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-0511" title="F2 | Separation of variables | ver. 0511"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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 \, {y} \cos\left(t\right) - 2 \, {y'} = 0 \hspace{2em} y( 0 )= -4" alt="-6 \, {y} \cos\left(t\right) - 2 \, {y'} = 0 \hspace{2em} y( 0 )= -4" title="-6 \, {y} \cos\left(t\right) - 2 \, {y'} = 0 \hspace{2em} y( 0 )= -4" data-latex="-6 \, {y} \cos\left(t\right) - 2 \, {y'} = 0 \hspace{2em} y( 0 )= -4"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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,%20%7By%7D%20%5Ccos%5Cleft(t%5Cright)%20-%202%20%5C,%20%7By'%7D%20=%200%20%5Chspace%7B2em%7D%20y(%200%20)=%20-4" alt="-6 \, {y} \cos\left(t\right) - 2 \, {y'} = 0 \hspace{2em} y( 0 )= -4" title="-6 \, {y} \cos\left(t\right) - 2 \, {y'} = 0 \hspace{2em} y( 0 )= -4" data-latex="-6 \, {y} \cos\left(t\right) - 2 \, {y'} = 0 \hspace{2em} y( 0 )= -4"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y} = -4 \, e^{\left(-3 \, \sin\left(t\right)\right)}" alt="{y} = -4 \, e^{\left(-3 \, \sin\left(t\right)\right)}" title="{y} = -4 \, e^{\left(-3 \, \sin\left(t\right)\right)}" data-latex="{y} = -4 \, e^{\left(-3 \, \sin\left(t\right)\right)}"/></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,%20e%5E%7B%5Cleft(-3%20%5C,%20%5Csin%5Cleft(t%5Cright)%5Cright)%7D" alt="{y} = -4 \, e^{\left(-3 \, \sin\left(t\right)\right)}" title="{y} = -4 \, e^{\left(-3 \, \sin\left(t\right)\right)}" data-latex="{y} = -4 \, e^{\left(-3 \, \sin\left(t\right)\right)}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-4527" title="F2 | Separation of variables | ver. 4527"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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} {y'} + \frac{4 \, t}{{y}} = -\frac{4}{{y}} \hspace{2em} y( -3 )= 3" alt="-2 \, {y} {y'} + \frac{4 \, t}{{y}} = -\frac{4}{{y}} \hspace{2em} y( -3 )= 3" title="-2 \, {y} {y'} + \frac{4 \, t}{{y}} = -\frac{4}{{y}} \hspace{2em} y( -3 )= 3" data-latex="-2 \, {y} {y'} + \frac{4 \, t}{{y}} = -\frac{4}{{y}} \hspace{2em} y( -3 )= 3"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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%7By'%7D%20+%20%5Cfrac%7B4%20%5C,%20t%7D%7B%7By%7D%7D%20=%20-%5Cfrac%7B4%7D%7B%7By%7D%7D%20%5Chspace%7B2em%7D%20y(%20-3%20)=%203" alt="-2 \, {y} {y'} + \frac{4 \, t}{{y}} = -\frac{4}{{y}} \hspace{2em} y( -3 )= 3" title="-2 \, {y} {y'} + \frac{4 \, t}{{y}} = -\frac{4}{{y}} \hspace{2em} y( -3 )= 3" data-latex="-2 \, {y} {y'} + \frac{4 \, t}{{y}} = -\frac{4}{{y}} \hspace{2em} y( -3 )= 3"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y} = \sqrt{t^{2} + 2 \, t + 6}" alt="{y} = \sqrt{t^{2} + 2 \, t + 6}" title="{y} = \sqrt{t^{2} + 2 \, t + 6}" data-latex="{y} = \sqrt{t^{2} + 2 \, t + 6}"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%7By%7D%20=%20%5Csqrt%7Bt%5E%7B2%7D%20+%202%20%5C,%20t%20+%206%7D" alt="{y} = \sqrt{t^{2} + 2 \, t + 6}" title="{y} = \sqrt{t^{2} + 2 \, t + 6}" data-latex="{y} = \sqrt{t^{2} + 2 \, t + 6}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-4406" title="F2 | Separation of variables | ver. 4406"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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 = 6 \, {y} \hspace{2em} y( 1 )= 4" alt="-2 \, {y'} t = 6 \, {y} \hspace{2em} y( 1 )= 4" title="-2 \, {y'} t = 6 \, {y} \hspace{2em} y( 1 )= 4" data-latex="-2 \, {y'} t = 6 \, {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;F2.&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%20t%20=%206%20%5C,%20%7By%7D%20%5Chspace%7B2em%7D%20y(%201%20)=%204" alt="-2 \, {y'} t = 6 \, {y} \hspace{2em} y( 1 )= 4" title="-2 \, {y'} t = 6 \, {y} \hspace{2em} y( 1 )= 4" data-latex="-2 \, {y'} t = 6 \, {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{4}{t^{3}}" alt="{y} = \frac{4}{t^{3}}" title="{y} = \frac{4}{t^{3}}" data-latex="{y} = \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%5Cfrac%7B4%7D%7Bt%5E%7B3%7D%7D" alt="{y} = \frac{4}{t^{3}}" title="{y} = \frac{4}{t^{3}}" data-latex="{y} = \frac{4}{t^{3}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-4343" title="F2 | Separation of variables | ver. 4343"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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?9 \, {y} = -3 \, {y'} t \hspace{2em} y( 3 )= \frac{4}{27}" alt="9 \, {y} = -3 \, {y'} t \hspace{2em} y( 3 )= \frac{4}{27}" title="9 \, {y} = -3 \, {y'} t \hspace{2em} y( 3 )= \frac{4}{27}" data-latex="9 \, {y} = -3 \, {y'} t \hspace{2em} y( 3 )= \frac{4}{27}"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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?9%20%5C,%20%7By%7D%20=%20-3%20%5C,%20%7By'%7D%20t%20%5Chspace%7B2em%7D%20y(%203%20)=%20%5Cfrac%7B4%7D%7B27%7D" alt="9 \, {y} = -3 \, {y'} t \hspace{2em} y( 3 )= \frac{4}{27}" title="9 \, {y} = -3 \, {y'} t \hspace{2em} y( 3 )= \frac{4}{27}" data-latex="9 \, {y} = -3 \, {y'} t \hspace{2em} y( 3 )= \frac{4}{27}"&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^{3}}" alt="{y} = \frac{4}{t^{3}}" title="{y} = \frac{4}{t^{3}}" data-latex="{y} = \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%5Cfrac%7B4%7D%7Bt%5E%7B3%7D%7D" alt="{y} = \frac{4}{t^{3}}" title="{y} = \frac{4}{t^{3}}" data-latex="{y} = \frac{4}{t^{3}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-3659" title="F2 | Separation of variables | ver. 3659"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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 \, {y} \cos\left(t\right) - 2 \, {y'} = 0 \hspace{2em} y( 0 )= 1" alt="-6 \, {y} \cos\left(t\right) - 2 \, {y'} = 0 \hspace{2em} y( 0 )= 1" title="-6 \, {y} \cos\left(t\right) - 2 \, {y'} = 0 \hspace{2em} y( 0 )= 1" data-latex="-6 \, {y} \cos\left(t\right) - 2 \, {y'} = 0 \hspace{2em} y( 0 )= 1"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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,%20%7By%7D%20%5Ccos%5Cleft(t%5Cright)%20-%202%20%5C,%20%7By'%7D%20=%200%20%5Chspace%7B2em%7D%20y(%200%20)=%201" alt="-6 \, {y} \cos\left(t\right) - 2 \, {y'} = 0 \hspace{2em} y( 0 )= 1" title="-6 \, {y} \cos\left(t\right) - 2 \, {y'} = 0 \hspace{2em} y( 0 )= 1" data-latex="-6 \, {y} \cos\left(t\right) - 2 \, {y'} = 0 \hspace{2em} y( 0 )= 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} = e^{\left(-3 \, \sin\left(t\right)\right)}" alt="{y} = e^{\left(-3 \, \sin\left(t\right)\right)}" title="{y} = e^{\left(-3 \, \sin\left(t\right)\right)}" data-latex="{y} = e^{\left(-3 \, \sin\left(t\right)\right)}"/></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=%20e%5E%7B%5Cleft(-3%20%5C,%20%5Csin%5Cleft(t%5Cright)%5Cright)%7D" alt="{y} = e^{\left(-3 \, \sin\left(t\right)\right)}" title="{y} = e^{\left(-3 \, \sin\left(t\right)\right)}" data-latex="{y} = e^{\left(-3 \, \sin\left(t\right)\right)}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-4936" title="F2 | Separation of variables | ver. 4936"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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} = 2 \, t {y'} \hspace{2em} y( -1 )= -4" alt="-4 \, {y} = 2 \, t {y'} \hspace{2em} y( -1 )= -4" title="-4 \, {y} = 2 \, t {y'} \hspace{2em} y( -1 )= -4" data-latex="-4 \, {y} = 2 \, 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;F2.&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=%202%20%5C,%20t%20%7By'%7D%20%5Chspace%7B2em%7D%20y(%20-1%20)=%20-4" alt="-4 \, {y} = 2 \, t {y'} \hspace{2em} y( -1 )= -4" title="-4 \, {y} = 2 \, t {y'} \hspace{2em} y( -1 )= -4" data-latex="-4 \, {y} = 2 \, 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{4}{t^{2}}" alt="{y} = -\frac{4}{t^{2}}" title="{y} = -\frac{4}{t^{2}}" data-latex="{y} = -\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%7B4%7D%7Bt%5E%7B2%7D%7D" alt="{y} = -\frac{4}{t^{2}}" title="{y} = -\frac{4}{t^{2}}" data-latex="{y} = -\frac{4}{t^{2}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-3524" title="F2 | Separation of variables | ver. 3524"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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}^{2} + \frac{3}{{y}} = -\frac{6 \, t}{{y}} \hspace{2em} y( -3 )= 4" alt="-3 \, {y'} {y}^{2} + \frac{3}{{y}} = -\frac{6 \, t}{{y}} \hspace{2em} y( -3 )= 4" title="-3 \, {y'} {y}^{2} + \frac{3}{{y}} = -\frac{6 \, t}{{y}} \hspace{2em} y( -3 )= 4" data-latex="-3 \, {y'} {y}^{2} + \frac{3}{{y}} = -\frac{6 \, t}{{y}} \hspace{2em} y( -3 )= 4"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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%7By%7D%5E%7B2%7D%20+%20%5Cfrac%7B3%7D%7B%7By%7D%7D%20=%20-%5Cfrac%7B6%20%5C,%20t%7D%7B%7By%7D%7D%20%5Chspace%7B2em%7D%20y(%20-3%20)=%204" alt="-3 \, {y'} {y}^{2} + \frac{3}{{y}} = -\frac{6 \, t}{{y}} \hspace{2em} y( -3 )= 4" title="-3 \, {y'} {y}^{2} + \frac{3}{{y}} = -\frac{6 \, t}{{y}} \hspace{2em} y( -3 )= 4" data-latex="-3 \, {y'} {y}^{2} + \frac{3}{{y}} = -\frac{6 \, t}{{y}} \hspace{2em} y( -3 )= 4"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y} = {\left(t^{2} + t + 58\right)}^{\frac{1}{3}}" alt="{y} = {\left(t^{2} + t + 58\right)}^{\frac{1}{3}}" title="{y} = {\left(t^{2} + t + 58\right)}^{\frac{1}{3}}" data-latex="{y} = {\left(t^{2} + t + 58\right)}^{\frac{1}{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%7B%5Cleft(t%5E%7B2%7D%20+%20t%20+%2058%5Cright)%7D%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D" alt="{y} = {\left(t^{2} + t + 58\right)}^{\frac{1}{3}}" title="{y} = {\left(t^{2} + t + 58\right)}^{\frac{1}{3}}" data-latex="{y} = {\left(t^{2} + t + 58\right)}^{\frac{1}{3}}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-2851" title="F2 | Separation of variables | ver. 2851"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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 \, {y} \sin\left(t\right) = 2 \, {y'} \hspace{2em} y( 0 )= -2 \, e^{\left(-3\right)}" alt="6 \, {y} \sin\left(t\right) = 2 \, {y'} \hspace{2em} y( 0 )= -2 \, e^{\left(-3\right)}" title="6 \, {y} \sin\left(t\right) = 2 \, {y'} \hspace{2em} y( 0 )= -2 \, e^{\left(-3\right)}" data-latex="6 \, {y} \sin\left(t\right) = 2 \, {y'} \hspace{2em} y( 0 )= -2 \, e^{\left(-3\right)}"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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,%20%7By%7D%20%5Csin%5Cleft(t%5Cright)%20=%202%20%5C,%20%7By'%7D%20%5Chspace%7B2em%7D%20y(%200%20)=%20-2%20%5C,%20e%5E%7B%5Cleft(-3%5Cright)%7D" alt="6 \, {y} \sin\left(t\right) = 2 \, {y'} \hspace{2em} y( 0 )= -2 \, e^{\left(-3\right)}" title="6 \, {y} \sin\left(t\right) = 2 \, {y'} \hspace{2em} y( 0 )= -2 \, e^{\left(-3\right)}" data-latex="6 \, {y} \sin\left(t\right) = 2 \, {y'} \hspace{2em} y( 0 )= -2 \, e^{\left(-3\right)}"&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 \, e^{\left(-3 \, \cos\left(t\right)\right)}" alt="{y} = -2 \, e^{\left(-3 \, \cos\left(t\right)\right)}" title="{y} = -2 \, e^{\left(-3 \, \cos\left(t\right)\right)}" data-latex="{y} = -2 \, e^{\left(-3 \, \cos\left(t\right)\right)}"/></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,%20e%5E%7B%5Cleft(-3%20%5C,%20%5Ccos%5Cleft(t%5Cright)%5Cright)%7D" alt="{y} = -2 \, e^{\left(-3 \, \cos\left(t\right)\right)}" title="{y} = -2 \, e^{\left(-3 \, \cos\left(t\right)\right)}" data-latex="{y} = -2 \, e^{\left(-3 \, \cos\left(t\right)\right)}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material></flow_mat></itemfeedback></item><item ident="F2-4790" title="F2 | Separation of variables | ver. 4790"><itemmetadata><qtimetadata><qtimetadatafield><fieldlabel>question_type</fieldlabel><fieldentry>essay_question</fieldentry></qtimetadatafield></qtimetadata></itemmetadata><presentation><material><mattextxml><div class="exercise-statement"><p><strong>F2.</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'} = -9 \, {y} \cos\left(t\right) \hspace{2em} y( 0 )= 2" alt="3 \, {y'} = -9 \, {y} \cos\left(t\right) \hspace{2em} y( 0 )= 2" title="3 \, {y'} = -9 \, {y} \cos\left(t\right) \hspace{2em} y( 0 )= 2" data-latex="3 \, {y'} = -9 \, {y} \cos\left(t\right) \hspace{2em} y( 0 )= 2"/></p></div></mattextxml><mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;F2.&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=%20-9%20%5C,%20%7By%7D%20%5Ccos%5Cleft(t%5Cright)%20%5Chspace%7B2em%7D%20y(%200%20)=%202" alt="3 \, {y'} = -9 \, {y} \cos\left(t\right) \hspace{2em} y( 0 )= 2" title="3 \, {y'} = -9 \, {y} \cos\left(t\right) \hspace{2em} y( 0 )= 2" data-latex="3 \, {y'} = -9 \, {y} \cos\left(t\right) \hspace{2em} y( 0 )= 2"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext></material><response_str ident="response1" rcardinality="Single"><render_fib><response_label ident="answer1" rshuffle="No"/></render_fib></response_str></presentation><itemfeedback ident="general_fb"><flow_mat><material><mattextxml><div class="exercise-answer"><h4>Partial Answer:</h4><p style="text-align:center;"><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y} = 2 \, e^{\left(-3 \, \sin\left(t\right)\right)}" alt="{y} = 2 \, e^{\left(-3 \, \sin\left(t\right)\right)}" title="{y} = 2 \, e^{\left(-3 \, \sin\left(t\right)\right)}" data-latex="{y} = 2 \, e^{\left(-3 \, \sin\left(t\right)\right)}"/></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,%20e%5E%7B%5Cleft(-3%20%5C,%20%5Csin%5Cleft(t%5Cright)%5Cright)%7D" alt="{y} = 2 \, e^{\left(-3 \, \sin\left(t\right)\right)}" title="{y} = 2 \, e^{\left(-3 \, \sin\left(t\right)\right)}" data-latex="{y} = 2 \, e^{\left(-3 \, \sin\left(t\right)\right)}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

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