0009.qti

<item ident="C5-5246" title="C5 | Non-homogeneous second-order linear ODE | ver. 5246">
  <itemmetadata>
    <qtimetadata>
      <qtimetadatafield>
        <fieldlabel>question_type</fieldlabel>
        <fieldentry>essay_question</fieldentry>
      </qtimetadatafield>
    </qtimetadata>
  </itemmetadata>
  <presentation>
    <material>
      <mattextxml>
        <div class="exercise-statement">
          <p>
            <strong>C5.</strong>
          </p>
          <p>Explain how to find the general solution to the given ODE.</p>
          <p style="text-align:center;">
            <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?0 = {y'} - 6 \, {y} + {y''} + 62 \, \cos\left(5 \, t\right) + 10 \, \sin\left(5 \, t\right)" alt="0 = {y'} - 6 \, {y} + {y''} + 62 \, \cos\left(5 \, t\right) + 10 \, \sin\left(5 \, t\right)" title="0 = {y'} - 6 \, {y} + {y''} + 62 \, \cos\left(5 \, t\right) + 10 \, \sin\left(5 \, t\right)" data-latex="0 = {y'} - 6 \, {y} + {y''} + 62 \, \cos\left(5 \, t\right) + 10 \, \sin\left(5 \, t\right)"/>
          </p>
        </div>
      </mattextxml>
      <mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;C5.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Explain how to find the general solution to the given ODE.&lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?0%20=%20%7By'%7D%20-%206%20%5C,%20%7By%7D%20+%20%7By''%7D%20+%2062%20%5C,%20%5Ccos%5Cleft(5%20%5C,%20t%5Cright)%20+%2010%20%5C,%20%5Csin%5Cleft(5%20%5C,%20t%5Cright)" alt="0 = {y'} - 6 \, {y} + {y''} + 62 \, \cos\left(5 \, t\right) + 10 \, \sin\left(5 \, t\right)" title="0 = {y'} - 6 \, {y} + {y''} + 62 \, \cos\left(5 \, t\right) + 10 \, \sin\left(5 \, t\right)" data-latex="0 = {y'} - 6 \, {y} + {y''} + 62 \, \cos\left(5 \, t\right) + 10 \, \sin\left(5 \, t\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} = k_{2} e^{\left(2 \, t\right)} + k_{1} e^{\left(-3 \, t\right)} + 2 \, \cos\left(5 \, t\right)" alt="{y} = k_{2} e^{\left(2 \, t\right)} + k_{1} e^{\left(-3 \, t\right)} + 2 \, \cos\left(5 \, t\right)" title="{y} = k_{2} e^{\left(2 \, t\right)} + k_{1} e^{\left(-3 \, t\right)} + 2 \, \cos\left(5 \, t\right)" data-latex="{y} = k_{2} e^{\left(2 \, t\right)} + k_{1} e^{\left(-3 \, t\right)} + 2 \, \cos\left(5 \, 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=%20k_%7B2%7D%20e%5E%7B%5Cleft(2%20%5C,%20t%5Cright)%7D%20+%20k_%7B1%7D%20e%5E%7B%5Cleft(-3%20%5C,%20t%5Cright)%7D%20+%202%20%5C,%20%5Ccos%5Cleft(5%20%5C,%20t%5Cright)" alt="{y} = k_{2} e^{\left(2 \, t\right)} + k_{1} e^{\left(-3 \, t\right)} + 2 \, \cos\left(5 \, t\right)" title="{y} = k_{2} e^{\left(2 \, t\right)} + k_{1} e^{\left(-3 \, t\right)} + 2 \, \cos\left(5 \, t\right)" data-latex="{y} = k_{2} e^{\left(2 \, t\right)} + k_{1} e^{\left(-3 \, t\right)} + 2 \, \cos\left(5 \, t\right)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

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