0007.qti

<item ident="N1-1204" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 1204">
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        <div class="exercise-statement">
          <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 - 2\right)} {y'} = -t^{2} - {\left(t - 6\right)} {y} - 1 \hspace{2em} x( -2 )= 3" alt="{\left(t + 5\right)} {\left(t - 2\right)} {y'} = -t^{2} - {\left(t - 6\right)} {y} - 1 \hspace{2em} x( -2 )= 3" title="{\left(t + 5\right)} {\left(t - 2\right)} {y'} = -t^{2} - {\left(t - 6\right)} {y} - 1 \hspace{2em} x( -2 )= 3" data-latex="{\left(t + 5\right)} {\left(t - 2\right)} {y'} = -t^{2} - {\left(t - 6\right)} {y} - 1 \hspace{2em} x( -2 )= 3"/>
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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-%202%5Cright)%7D%20%7By'%7D%20=%20-t%5E%7B2%7D%20-%20%7B%5Cleft(t%20-%206%5Cright)%7D%20%7By%7D%20-%201%20%5Chspace%7B2em%7D%20x(%20-2%20)=%203" alt="{\left(t + 5\right)} {\left(t - 2\right)} {y'} = -t^{2} - {\left(t - 6\right)} {y} - 1 \hspace{2em} x( -2 )= 3" title="{\left(t + 5\right)} {\left(t - 2\right)} {y'} = -t^{2} - {\left(t - 6\right)} {y} - 1 \hspace{2em} x( -2 )= 3" data-latex="{\left(t + 5\right)} {\left(t - 2\right)} {y'} = -t^{2} - {\left(t - 6\right)} {y} - 1 \hspace{2em} x( -2 )= 3"&gt;
  &lt;/p&gt;
&lt;/div&gt;

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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?(-5,2)" alt="(-5,2)" title="(-5,2)" data-latex="(-5,2)"/>
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  &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?(-5,2)" alt="(-5,2)" title="(-5,2)" data-latex="(-5,2)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

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