0007.qti

<item ident="X2-5707" title="X2 | Existence/uniqueness theorem for linear IVPs | ver. 5707">
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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?y e^{t} - 2 \, {y''} = -{\left(t + 5\right)} {\left(t - 1\right)} {y'''} - t + 5 \hspace{2em} x( -3 )= 3" alt="y e^{t} - 2 \, {y''} = -{\left(t + 5\right)} {\left(t - 1\right)} {y'''} - t + 5 \hspace{2em} x( -3 )= 3" title="y e^{t} - 2 \, {y''} = -{\left(t + 5\right)} {\left(t - 1\right)} {y'''} - t + 5 \hspace{2em} x( -3 )= 3" data-latex="y e^{t} - 2 \, {y''} = -{\left(t + 5\right)} {\left(t - 1\right)} {y'''} - t + 5 \hspace{2em} x( -3 )= 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?y%20e%5E%7Bt%7D%20-%202%20%5C,%20%7By''%7D%20=%20-%7B%5Cleft(t%20+%205%5Cright)%7D%20%7B%5Cleft(t%20-%201%5Cright)%7D%20%7By'''%7D%20-%20t%20+%205%20%5Chspace%7B2em%7D%20x(%20-3%20)=%203" alt="y e^{t} - 2 \, {y''} = -{\left(t + 5\right)} {\left(t - 1\right)} {y'''} - t + 5 \hspace{2em} x( -3 )= 3" title="y e^{t} - 2 \, {y''} = -{\left(t + 5\right)} {\left(t - 1\right)} {y'''} - t + 5 \hspace{2em} x( -3 )= 3" data-latex="y e^{t} - 2 \, {y''} = -{\left(t + 5\right)} {\left(t - 1\right)} {y'''} - t + 5 \hspace{2em} x( -3 )= 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?(-5,1)" alt="(-5,1)" title="(-5,1)" data-latex="(-5,1)"/>
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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?(-5,1)" alt="(-5,1)" title="(-5,1)" data-latex="(-5,1)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

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