0000.qti

<item ident="N1-2568" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 2568">
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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 + 4\right)} {\left(t - 1\right)} {y'} - e^{\left(3 \, t\right)} = {\left(t - 6\right)} {y} e^{t} \hspace{2em} x( -3 )= -8" alt="-{\left(t + 4\right)} {\left(t - 1\right)} {y'} - e^{\left(3 \, t\right)} = {\left(t - 6\right)} {y} e^{t} \hspace{2em} x( -3 )= -8" title="-{\left(t + 4\right)} {\left(t - 1\right)} {y'} - e^{\left(3 \, t\right)} = {\left(t - 6\right)} {y} e^{t} \hspace{2em} x( -3 )= -8" data-latex="-{\left(t + 4\right)} {\left(t - 1\right)} {y'} - e^{\left(3 \, t\right)} = {\left(t - 6\right)} {y} e^{t} \hspace{2em} x( -3 )= -8"/>
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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+%204%5Cright)%7D%20%7B%5Cleft(t%20-%201%5Cright)%7D%20%7By'%7D%20-%20e%5E%7B%5Cleft(3%20%5C,%20t%5Cright)%7D%20=%20%7B%5Cleft(t%20-%206%5Cright)%7D%20%7By%7D%20e%5E%7Bt%7D%20%5Chspace%7B2em%7D%20x(%20-3%20)=%20-8" alt="-{\left(t + 4\right)} {\left(t - 1\right)} {y'} - e^{\left(3 \, t\right)} = {\left(t - 6\right)} {y} e^{t} \hspace{2em} x( -3 )= -8" title="-{\left(t + 4\right)} {\left(t - 1\right)} {y'} - e^{\left(3 \, t\right)} = {\left(t - 6\right)} {y} e^{t} \hspace{2em} x( -3 )= -8" data-latex="-{\left(t + 4\right)} {\left(t - 1\right)} {y'} - e^{\left(3 \, t\right)} = {\left(t - 6\right)} {y} e^{t} \hspace{2em} x( -3 )= -8"&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?(-4,1)" alt="(-4,1)" title="(-4,1)" data-latex="(-4,1)"/>
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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?(-4,1)" alt="(-4,1)" title="(-4,1)" data-latex="(-4,1)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

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