0009.qti

<item ident="X2-7628" title="X2 | Existence/uniqueness theorem for linear IVPs | ver. 7628">
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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 + 5\right)} {\left(t - 2\right)} y + 2 \, {y''} - e^{\left(3 \, t\right)} = {\left(t - 5\right)} {y'''} e^{t} \hspace{2em} x( 6 )= 3" alt="-{\left(t + 5\right)} {\left(t - 2\right)} y + 2 \, {y''} - e^{\left(3 \, t\right)} = {\left(t - 5\right)} {y'''} e^{t} \hspace{2em} x( 6 )= 3" title="-{\left(t + 5\right)} {\left(t - 2\right)} y + 2 \, {y''} - e^{\left(3 \, t\right)} = {\left(t - 5\right)} {y'''} e^{t} \hspace{2em} x( 6 )= 3" data-latex="-{\left(t + 5\right)} {\left(t - 2\right)} y + 2 \, {y''} - e^{\left(3 \, t\right)} = {\left(t - 5\right)} {y'''} e^{t} \hspace{2em} x( 6 )= 3"/>
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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+%205%5Cright)%7D%20%7B%5Cleft(t%20-%202%5Cright)%7D%20y%20+%202%20%5C,%20%7By''%7D%20-%20e%5E%7B%5Cleft(3%20%5C,%20t%5Cright)%7D%20=%20%7B%5Cleft(t%20-%205%5Cright)%7D%20%7By'''%7D%20e%5E%7Bt%7D%20%5Chspace%7B2em%7D%20x(%206%20)=%203" alt="-{\left(t + 5\right)} {\left(t - 2\right)} y + 2 \, {y''} - e^{\left(3 \, t\right)} = {\left(t - 5\right)} {y'''} e^{t} \hspace{2em} x( 6 )= 3" title="-{\left(t + 5\right)} {\left(t - 2\right)} y + 2 \, {y''} - e^{\left(3 \, t\right)} = {\left(t - 5\right)} {y'''} e^{t} \hspace{2em} x( 6 )= 3" data-latex="-{\left(t + 5\right)} {\left(t - 2\right)} y + 2 \, {y''} - e^{\left(3 \, t\right)} = {\left(t - 5\right)} {y'''} e^{t} \hspace{2em} x( 6 )= 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,+\infty)" alt="(5,+\infty)" title="(5,+\infty)" data-latex="(5,+\infty)"/>
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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,+%5Cinfty)" alt="(5,+\infty)" title="(5,+\infty)" data-latex="(5,+\infty)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

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