0001.qti

<item ident="X2-0503" title="X2 | Existence/uniqueness theorem for linear IVPs | ver. 0503">
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  <presentation>
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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)} {y'''} e^{t} = {\left(t + 4\right)} {\left(t + 2\right)} y + 3 \, {y''} + e^{\left(-5 \, t\right)} \hspace{2em} x( 9 )= 2" alt="-{\left(t - 5\right)} {y'''} e^{t} = {\left(t + 4\right)} {\left(t + 2\right)} y + 3 \, {y''} + e^{\left(-5 \, t\right)} \hspace{2em} x( 9 )= 2" title="-{\left(t - 5\right)} {y'''} e^{t} = {\left(t + 4\right)} {\left(t + 2\right)} y + 3 \, {y''} + e^{\left(-5 \, t\right)} \hspace{2em} x( 9 )= 2" data-latex="-{\left(t - 5\right)} {y'''} e^{t} = {\left(t + 4\right)} {\left(t + 2\right)} y + 3 \, {y''} + e^{\left(-5 \, t\right)} \hspace{2em} x( 9 )= 2"/>
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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%7By'''%7D%20e%5E%7Bt%7D%20=%20%7B%5Cleft(t%20+%204%5Cright)%7D%20%7B%5Cleft(t%20+%202%5Cright)%7D%20y%20+%203%20%5C,%20%7By''%7D%20+%20e%5E%7B%5Cleft(-5%20%5C,%20t%5Cright)%7D%20%5Chspace%7B2em%7D%20x(%209%20)=%202" alt="-{\left(t - 5\right)} {y'''} e^{t} = {\left(t + 4\right)} {\left(t + 2\right)} y + 3 \, {y''} + e^{\left(-5 \, t\right)} \hspace{2em} x( 9 )= 2" title="-{\left(t - 5\right)} {y'''} e^{t} = {\left(t + 4\right)} {\left(t + 2\right)} y + 3 \, {y''} + e^{\left(-5 \, t\right)} \hspace{2em} x( 9 )= 2" data-latex="-{\left(t - 5\right)} {y'''} e^{t} = {\left(t + 4\right)} {\left(t + 2\right)} y + 3 \, {y''} + e^{\left(-5 \, t\right)} \hspace{2em} x( 9 )= 2"&gt;
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&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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        <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?(5,+%5Cinfty)" alt="(5,+\infty)" title="(5,+\infty)" data-latex="(5,+\infty)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

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