0003.qti

<item ident="X2-0316" title="X2 | Existence/uniqueness theorem for linear IVPs | ver. 0316">
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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?t^{2} + 5 \, {y''} + 25 = -{\left(t + 6\right)} {\left(t - 6\right)} {y'''} - t y e^{t} \hspace{2em} x( -1 )= -10" alt="t^{2} + 5 \, {y''} + 25 = -{\left(t + 6\right)} {\left(t - 6\right)} {y'''} - t y e^{t} \hspace{2em} x( -1 )= -10" title="t^{2} + 5 \, {y''} + 25 = -{\left(t + 6\right)} {\left(t - 6\right)} {y'''} - t y e^{t} \hspace{2em} x( -1 )= -10" data-latex="t^{2} + 5 \, {y''} + 25 = -{\left(t + 6\right)} {\left(t - 6\right)} {y'''} - t y e^{t} \hspace{2em} x( -1 )= -10"/>
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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?t%5E%7B2%7D%20+%205%20%5C,%20%7By''%7D%20+%2025%20=%20-%7B%5Cleft(t%20+%206%5Cright)%7D%20%7B%5Cleft(t%20-%206%5Cright)%7D%20%7By'''%7D%20-%20t%20y%20e%5E%7Bt%7D%20%5Chspace%7B2em%7D%20x(%20-1%20)=%20-10" alt="t^{2} + 5 \, {y''} + 25 = -{\left(t + 6\right)} {\left(t - 6\right)} {y'''} - t y e^{t} \hspace{2em} x( -1 )= -10" title="t^{2} + 5 \, {y''} + 25 = -{\left(t + 6\right)} {\left(t - 6\right)} {y'''} - t y e^{t} \hspace{2em} x( -1 )= -10" data-latex="t^{2} + 5 \, {y''} + 25 = -{\left(t + 6\right)} {\left(t - 6\right)} {y'''} - t y e^{t} \hspace{2em} x( -1 )= -10"&gt;
  &lt;/p&gt;
&lt;/div&gt;

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  <itemfeedback ident="general_fb">
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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?(-6,6)" alt="(-6,6)" title="(-6,6)" data-latex="(-6,6)"/>
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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?(-6,6)" alt="(-6,6)" title="(-6,6)" data-latex="(-6,6)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

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