0001.qti

<item ident="N1-3781" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 3781">
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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 + 6\right)} {\left(t - 1\right)} {y} - {\left(t^{2} + 1\right)} {y'} = {\left(t - 6\right)} e^{t} \hspace{2em} x( 5 )= -1" alt="-{\left(t + 6\right)} {\left(t - 1\right)} {y} - {\left(t^{2} + 1\right)} {y'} = {\left(t - 6\right)} e^{t} \hspace{2em} x( 5 )= -1" title="-{\left(t + 6\right)} {\left(t - 1\right)} {y} - {\left(t^{2} + 1\right)} {y'} = {\left(t - 6\right)} e^{t} \hspace{2em} x( 5 )= -1" data-latex="-{\left(t + 6\right)} {\left(t - 1\right)} {y} - {\left(t^{2} + 1\right)} {y'} = {\left(t - 6\right)} e^{t} \hspace{2em} x( 5 )= -1"/>
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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+%206%5Cright)%7D%20%7B%5Cleft(t%20-%201%5Cright)%7D%20%7By%7D%20-%20%7B%5Cleft(t%5E%7B2%7D%20+%201%5Cright)%7D%20%7By'%7D%20=%20%7B%5Cleft(t%20-%206%5Cright)%7D%20e%5E%7Bt%7D%20%5Chspace%7B2em%7D%20x(%205%20)=%20-1" alt="-{\left(t + 6\right)} {\left(t - 1\right)} {y} - {\left(t^{2} + 1\right)} {y'} = {\left(t - 6\right)} e^{t} \hspace{2em} x( 5 )= -1" title="-{\left(t + 6\right)} {\left(t - 1\right)} {y} - {\left(t^{2} + 1\right)} {y'} = {\left(t - 6\right)} e^{t} \hspace{2em} x( 5 )= -1" data-latex="-{\left(t + 6\right)} {\left(t - 1\right)} {y} - {\left(t^{2} + 1\right)} {y'} = {\left(t - 6\right)} e^{t} \hspace{2em} x( 5 )= -1"&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?(-\infty,+\infty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\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?(-%5Cinfty,+%5Cinfty)" alt="(-\infty,+\infty)" title="(-\infty,+\infty)" data-latex="(-\infty,+\infty)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

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