0004.qti

<item ident="X2-3195" title="X2 | Existence/uniqueness theorem for linear IVPs | ver. 3195">
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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?0 = -{\left(t + 2\right)} {\left(t - 5\right)} y - {\left(t + 5\right)} {y'''} e^{t} + 5 \, {y''} - e^{\left(2 \, t\right)} \hspace{2em} x( -7 )= -1" alt="0 = -{\left(t + 2\right)} {\left(t - 5\right)} y - {\left(t + 5\right)} {y'''} e^{t} + 5 \, {y''} - e^{\left(2 \, t\right)} \hspace{2em} x( -7 )= -1" title="0 = -{\left(t + 2\right)} {\left(t - 5\right)} y - {\left(t + 5\right)} {y'''} e^{t} + 5 \, {y''} - e^{\left(2 \, t\right)} \hspace{2em} x( -7 )= -1" data-latex="0 = -{\left(t + 2\right)} {\left(t - 5\right)} y - {\left(t + 5\right)} {y'''} e^{t} + 5 \, {y''} - e^{\left(2 \, t\right)} \hspace{2em} x( -7 )= -1"/>
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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?0%20=%20-%7B%5Cleft(t%20+%202%5Cright)%7D%20%7B%5Cleft(t%20-%205%5Cright)%7D%20y%20-%20%7B%5Cleft(t%20+%205%5Cright)%7D%20%7By'''%7D%20e%5E%7Bt%7D%20+%205%20%5C,%20%7By''%7D%20-%20e%5E%7B%5Cleft(2%20%5C,%20t%5Cright)%7D%20%5Chspace%7B2em%7D%20x(%20-7%20)=%20-1" alt="0 = -{\left(t + 2\right)} {\left(t - 5\right)} y - {\left(t + 5\right)} {y'''} e^{t} + 5 \, {y''} - e^{\left(2 \, t\right)} \hspace{2em} x( -7 )= -1" title="0 = -{\left(t + 2\right)} {\left(t - 5\right)} y - {\left(t + 5\right)} {y'''} e^{t} + 5 \, {y''} - e^{\left(2 \, t\right)} \hspace{2em} x( -7 )= -1" data-latex="0 = -{\left(t + 2\right)} {\left(t - 5\right)} y - {\left(t + 5\right)} {y'''} e^{t} + 5 \, {y''} - e^{\left(2 \, t\right)} \hspace{2em} x( -7 )= -1"&gt;
  &lt;/p&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,-5)" alt="(-\infty,-5)" title="(-\infty,-5)" data-latex="(-\infty,-5)"/>
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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?(-%5Cinfty,-5)" alt="(-\infty,-5)" title="(-\infty,-5)" data-latex="(-\infty,-5)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

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