0000.qti

<item ident="X2-0368" title="X2 | Existence/uniqueness theorem for linear IVPs | ver. 0368">
  <itemmetadata>
    <qtimetadata>
      <qtimetadatafield>
        <fieldlabel>question_type</fieldlabel>
        <fieldentry>essay_question</fieldentry>
      </qtimetadatafield>
    </qtimetadata>
  </itemmetadata>
  <presentation>
    <material>
      <mattextxml>
        <div class="exercise-statement">
          <p>
            <strong>X2.</strong>
          </p>
          <p> Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following 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?-{\left(t + 4\right)} {\left(t - 5\right)} {y'''} - {\left(t - 1\right)} y e^{t} = t^{2} + 5 \, {y''} + 25 \hspace{2em} x( 1 )= 7" alt="-{\left(t + 4\right)} {\left(t - 5\right)} {y'''} - {\left(t - 1\right)} y e^{t} = t^{2} + 5 \, {y''} + 25 \hspace{2em} x( 1 )= 7" title="-{\left(t + 4\right)} {\left(t - 5\right)} {y'''} - {\left(t - 1\right)} y e^{t} = t^{2} + 5 \, {y''} + 25 \hspace{2em} x( 1 )= 7" data-latex="-{\left(t + 4\right)} {\left(t - 5\right)} {y'''} - {\left(t - 1\right)} y e^{t} = t^{2} + 5 \, {y''} + 25 \hspace{2em} x( 1 )= 7"/>
          </p>
        </div>
      </mattextxml>
      <mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;X2.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Find the largest interval for which the Existence and Uniqueness Theorem for Linear IVPs guarantees a unique solution for the following 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?-%7B%5Cleft(t%20+%204%5Cright)%7D%20%7B%5Cleft(t%20-%205%5Cright)%7D%20%7By'''%7D%20-%20%7B%5Cleft(t%20-%201%5Cright)%7D%20y%20e%5E%7Bt%7D%20=%20t%5E%7B2%7D%20+%205%20%5C,%20%7By''%7D%20+%2025%20%5Chspace%7B2em%7D%20x(%201%20)=%207" alt="-{\left(t + 4\right)} {\left(t - 5\right)} {y'''} - {\left(t - 1\right)} y e^{t} = t^{2} + 5 \, {y''} + 25 \hspace{2em} x( 1 )= 7" title="-{\left(t + 4\right)} {\left(t - 5\right)} {y'''} - {\left(t - 1\right)} y e^{t} = t^{2} + 5 \, {y''} + 25 \hspace{2em} x( 1 )= 7" data-latex="-{\left(t + 4\right)} {\left(t - 5\right)} {y'''} - {\left(t - 1\right)} y e^{t} = t^{2} + 5 \, {y''} + 25 \hspace{2em} x( 1 )= 7"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext>
    </material>
    <response_str ident="response1" rcardinality="Single">
      <render_fib>
        <response_label ident="answer1" rshuffle="No"/>
      </render_fib>
    </response_str>
  </presentation>
  <itemfeedback ident="general_fb">
    <flow_mat>
      <material>
        <mattextxml>
          <div class="exercise-answer">
            <h4>Partial Answer:</h4>
            <p style="text-align:center;">
              <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-4,5)" alt="(-4,5)" title="(-4,5)" data-latex="(-4,5)"/>
            </p>
          </div>
        </mattextxml>
        <mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(-4,5)" alt="(-4,5)" title="(-4,5)" data-latex="(-4,5)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

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