0005.qti

<item ident="C4-2691" title="C4 | Homogeneous second-order linear IVP | ver. 2691">
  <itemmetadata>
    <qtimetadata>
      <qtimetadatafield>
        <fieldlabel>question_type</fieldlabel>
        <fieldentry>essay_question</fieldentry>
      </qtimetadatafield>
    </qtimetadata>
  </itemmetadata>
  <presentation>
    <material>
      <mattextxml>
        <div class="exercise-statement">
          <p>
            <strong>C4.</strong>
          </p>
          <p>Explain how to find the particular solution to each given IVP.</p>
          <ol type="a">
            <li>
              <p style="text-align:center;">
                <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?0 = -{x''} - 3 \, {x} + 4 \, {x'} \hspace{2em} {x} (0)= 4 , {x} '(0)= 10" alt="0 = -{x''} - 3 \, {x} + 4 \, {x'} \hspace{2em} {x} (0)= 4 , {x} '(0)= 10" title="0 = -{x''} - 3 \, {x} + 4 \, {x'} \hspace{2em} {x} (0)= 4 , {x} '(0)= 10" data-latex="0 = -{x''} - 3 \, {x} + 4 \, {x'} \hspace{2em} {x} (0)= 4 , {x} '(0)= 10"/>
              </p>
            </li>
            <li>
              <p style="text-align:center;">
                <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-100 \, {y} = {y''} \hspace{2em} {y} (0)= 3 , {y} '(0)= -30" alt="-100 \, {y} = {y''} \hspace{2em} {y} (0)= 3 , {y} '(0)= -30" title="-100 \, {y} = {y''} \hspace{2em} {y} (0)= 3 , {y} '(0)= -30" data-latex="-100 \, {y} = {y''} \hspace{2em} {y} (0)= 3 , {y} '(0)= -30"/>
              </p>
            </li>
          </ol>
        </div>
      </mattextxml>
      <mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;C4.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Explain how to find the particular solution to each given IVP.&lt;/p&gt;
  &lt;ol type="a"&gt;
    &lt;li&gt;
      &lt;p 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-%7Bx''%7D%20-%203%20%5C,%20%7Bx%7D%20+%204%20%5C,%20%7Bx'%7D%20%5Chspace%7B2em%7D%20%7Bx%7D%20(0)=%204%20,%20%7Bx%7D%20'(0)=%2010" alt="0 = -{x''} - 3 \, {x} + 4 \, {x'} \hspace{2em} {x} (0)= 4 , {x} '(0)= 10" title="0 = -{x''} - 3 \, {x} + 4 \, {x'} \hspace{2em} {x} (0)= 4 , {x} '(0)= 10" data-latex="0 = -{x''} - 3 \, {x} + 4 \, {x'} \hspace{2em} {x} (0)= 4 , {x} '(0)= 10"&gt;
      &lt;/p&gt;
    &lt;/li&gt;
    &lt;li&gt;
      &lt;p style="text-align:center;"&gt;
        &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-100%20%5C,%20%7By%7D%20=%20%7By''%7D%20%5Chspace%7B2em%7D%20%7By%7D%20(0)=%203%20,%20%7By%7D%20'(0)=%20-30" alt="-100 \, {y} = {y''} \hspace{2em} {y} (0)= 3 , {y} '(0)= -30" title="-100 \, {y} = {y''} \hspace{2em} {y} (0)= 3 , {y} '(0)= -30" data-latex="-100 \, {y} = {y''} \hspace{2em} {y} (0)= 3 , {y} '(0)= -30"&gt;
      &lt;/p&gt;
    &lt;/li&gt;
  &lt;/ol&gt;
&lt;/div&gt;

</mattext>
    </material>
    <response_str ident="response1" rcardinality="Single">
      <render_fib>
        <response_label ident="answer1" rshuffle="No"/>
      </render_fib>
    </response_str>
  </presentation>
  <itemfeedback ident="general_fb">
    <flow_mat>
      <material>
        <mattextxml>
          <div class="exercise-answer">
            <h4>Partial Answer:</h4>
            <p style="text-align:center;">
              <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{x} = 3 \, e^{\left(3 \, t\right)} + e^{t}" alt="{x} = 3 \, e^{\left(3 \, t\right)} + e^{t}" title="{x} = 3 \, e^{\left(3 \, t\right)} + e^{t}" data-latex="{x} = 3 \, e^{\left(3 \, t\right)} + e^{t}"/>
            </p>
            <p style="text-align:center;">
              <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y} = 3 \, \cos\left(10 \, t\right) - 3 \, \sin\left(10 \, t\right)" alt="{y} = 3 \, \cos\left(10 \, t\right) - 3 \, \sin\left(10 \, t\right)" title="{y} = 3 \, \cos\left(10 \, t\right) - 3 \, \sin\left(10 \, t\right)" data-latex="{y} = 3 \, \cos\left(10 \, t\right) - 3 \, \sin\left(10 \, 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?%7Bx%7D%20=%203%20%5C,%20e%5E%7B%5Cleft(3%20%5C,%20t%5Cright)%7D%20+%20e%5E%7Bt%7D" alt="{x} = 3 \, e^{\left(3 \, t\right)} + e^{t}" title="{x} = 3 \, e^{\left(3 \, t\right)} + e^{t}" data-latex="{x} = 3 \, e^{\left(3 \, t\right)} + e^{t}"&gt;
  &lt;/p&gt;
  &lt;p style="text-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,%20%5Ccos%5Cleft(10%20%5C,%20t%5Cright)%20-%203%20%5C,%20%5Csin%5Cleft(10%20%5C,%20t%5Cright)" alt="{y} = 3 \, \cos\left(10 \, t\right) - 3 \, \sin\left(10 \, t\right)" title="{y} = 3 \, \cos\left(10 \, t\right) - 3 \, \sin\left(10 \, t\right)" data-latex="{y} = 3 \, \cos\left(10 \, t\right) - 3 \, \sin\left(10 \, t\right)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

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