0011.qti

<item ident="C4-1809" title="C4 | Homogeneous second-order linear IVP | ver. 1809">
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  <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?-{x''} = 4 \, {x} \hspace{2em} {x} (0)= -4 , {x} '(0)= 0" alt="-{x''} = 4 \, {x} \hspace{2em} {x} (0)= -4 , {x} '(0)= 0" title="-{x''} = 4 \, {x} \hspace{2em} {x} (0)= -4 , {x} '(0)= 0" data-latex="-{x''} = 4 \, {x} \hspace{2em} {x} (0)= -4 , {x} '(0)= 0"/>
              </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?2 \, {y} = -{y''} + 3 \, {y'} \hspace{2em} {y} (0)= -8 , {y} '(0)= -13" alt="2 \, {y} = -{y''} + 3 \, {y'} \hspace{2em} {y} (0)= -8 , {y} '(0)= -13" title="2 \, {y} = -{y''} + 3 \, {y'} \hspace{2em} {y} (0)= -8 , {y} '(0)= -13" data-latex="2 \, {y} = -{y''} + 3 \, {y'} \hspace{2em} {y} (0)= -8 , {y} '(0)= -13"/>
              </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?-%7Bx''%7D%20=%204%20%5C,%20%7Bx%7D%20%5Chspace%7B2em%7D%20%7Bx%7D%20(0)=%20-4%20,%20%7Bx%7D%20'(0)=%200" alt="-{x''} = 4 \, {x} \hspace{2em} {x} (0)= -4 , {x} '(0)= 0" title="-{x''} = 4 \, {x} \hspace{2em} {x} (0)= -4 , {x} '(0)= 0" data-latex="-{x''} = 4 \, {x} \hspace{2em} {x} (0)= -4 , {x} '(0)= 0"&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?2%20%5C,%20%7By%7D%20=%20-%7By''%7D%20+%203%20%5C,%20%7By'%7D%20%5Chspace%7B2em%7D%20%7By%7D%20(0)=%20-8%20,%20%7By%7D%20'(0)=%20-13" alt="2 \, {y} = -{y''} + 3 \, {y'} \hspace{2em} {y} (0)= -8 , {y} '(0)= -13" title="2 \, {y} = -{y''} + 3 \, {y'} \hspace{2em} {y} (0)= -8 , {y} '(0)= -13" data-latex="2 \, {y} = -{y''} + 3 \, {y'} \hspace{2em} {y} (0)= -8 , {y} '(0)= -13"&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} = -4 \, \cos\left(2 \, t\right)" alt="{x} = -4 \, \cos\left(2 \, t\right)" title="{x} = -4 \, \cos\left(2 \, t\right)" data-latex="{x} = -4 \, \cos\left(2 \, t\right)"/>
            </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} = -5 \, e^{\left(2 \, t\right)} - 3 \, e^{t}" alt="{y} = -5 \, e^{\left(2 \, t\right)} - 3 \, e^{t}" title="{y} = -5 \, e^{\left(2 \, t\right)} - 3 \, e^{t}" data-latex="{y} = -5 \, e^{\left(2 \, t\right)} - 3 \, e^{t}"/>
            </p>
          </div>
        </mattextxml>
        <mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%7Bx%7D%20=%20-4%20%5C,%20%5Ccos%5Cleft(2%20%5C,%20t%5Cright)" alt="{x} = -4 \, \cos\left(2 \, t\right)" title="{x} = -4 \, \cos\left(2 \, t\right)" data-latex="{x} = -4 \, \cos\left(2 \, t\right)"&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=%20-5%20%5C,%20e%5E%7B%5Cleft(2%20%5C,%20t%5Cright)%7D%20-%203%20%5C,%20e%5E%7Bt%7D" alt="{y} = -5 \, e^{\left(2 \, t\right)} - 3 \, e^{t}" title="{y} = -5 \, e^{\left(2 \, t\right)} - 3 \, e^{t}" data-latex="{y} = -5 \, e^{\left(2 \, t\right)} - 3 \, e^{t}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext>
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  </itemfeedback>
</item>