0005.qti

<item ident="X2-3351" title="X2 | Existence/uniqueness theorem for linear IVPs | ver. 3351">
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        <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 - 2\right)} {y''} - e^{\left(-5 \, t\right)} = -{y'} \hspace{2em} x( 0 )= 5" alt="-{\left(t + 4\right)} {\left(t - 5\right)} y - {\left(t - 2\right)} {y''} - e^{\left(-5 \, t\right)} = -{y'} \hspace{2em} x( 0 )= 5" title="-{\left(t + 4\right)} {\left(t - 5\right)} y - {\left(t - 2\right)} {y''} - e^{\left(-5 \, t\right)} = -{y'} \hspace{2em} x( 0 )= 5" data-latex="-{\left(t + 4\right)} {\left(t - 5\right)} y - {\left(t - 2\right)} {y''} - e^{\left(-5 \, t\right)} = -{y'} \hspace{2em} x( 0 )= 5"/>
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      <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%20y%20-%20%7B%5Cleft(t%20-%202%5Cright)%7D%20%7By''%7D%20-%20e%5E%7B%5Cleft(-5%20%5C,%20t%5Cright)%7D%20=%20-%7By'%7D%20%5Chspace%7B2em%7D%20x(%200%20)=%205" alt="-{\left(t + 4\right)} {\left(t - 5\right)} y - {\left(t - 2\right)} {y''} - e^{\left(-5 \, t\right)} = -{y'} \hspace{2em} x( 0 )= 5" title="-{\left(t + 4\right)} {\left(t - 5\right)} y - {\left(t - 2\right)} {y''} - e^{\left(-5 \, t\right)} = -{y'} \hspace{2em} x( 0 )= 5" data-latex="-{\left(t + 4\right)} {\left(t - 5\right)} y - {\left(t - 2\right)} {y''} - e^{\left(-5 \, t\right)} = -{y'} \hspace{2em} x( 0 )= 5"&gt;
  &lt;/p&gt;
&lt;/div&gt;

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  <itemfeedback ident="general_fb">
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            <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?(-\infty,2)" alt="(-\infty,2)" title="(-\infty,2)" data-latex="(-\infty,2)"/>
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        <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?(-%5Cinfty,2)" alt="(-\infty,2)" title="(-\infty,2)" data-latex="(-\infty,2)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

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