0005.qti

<item ident="N1-1378" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 1378">
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          <p>
            <strong>N1.</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 + 5\right)} {\left(t - 5\right)} {y} + t^{2} + 1 = -{\left(t + 2\right)} {y'} e^{t} \hspace{2em} x( 0 )= -5" alt="{\left(t + 5\right)} {\left(t - 5\right)} {y} + t^{2} + 1 = -{\left(t + 2\right)} {y'} e^{t} \hspace{2em} x( 0 )= -5" title="{\left(t + 5\right)} {\left(t - 5\right)} {y} + t^{2} + 1 = -{\left(t + 2\right)} {y'} e^{t} \hspace{2em} x( 0 )= -5" data-latex="{\left(t + 5\right)} {\left(t - 5\right)} {y} + t^{2} + 1 = -{\left(t + 2\right)} {y'} e^{t} \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;N1.&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+%205%5Cright)%7D%20%7B%5Cleft(t%20-%205%5Cright)%7D%20%7By%7D%20+%20t%5E%7B2%7D%20+%201%20=%20-%7B%5Cleft(t%20+%202%5Cright)%7D%20%7By'%7D%20e%5E%7Bt%7D%20%5Chspace%7B2em%7D%20x(%200%20)=%20-5" alt="{\left(t + 5\right)} {\left(t - 5\right)} {y} + t^{2} + 1 = -{\left(t + 2\right)} {y'} e^{t} \hspace{2em} x( 0 )= -5" title="{\left(t + 5\right)} {\left(t - 5\right)} {y} + t^{2} + 1 = -{\left(t + 2\right)} {y'} e^{t} \hspace{2em} x( 0 )= -5" data-latex="{\left(t + 5\right)} {\left(t - 5\right)} {y} + t^{2} + 1 = -{\left(t + 2\right)} {y'} e^{t} \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?(-2,+\infty)" alt="(-2,+\infty)" title="(-2,+\infty)" data-latex="(-2,+\infty)"/>
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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?(-2,+%5Cinfty)" alt="(-2,+\infty)" title="(-2,+\infty)" data-latex="(-2,+\infty)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

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