0011.qti

<item ident="X2-9528" title="X2 | Existence/uniqueness theorem for linear IVPs | ver. 9528">
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          <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?3 \, {y''} = {\left(t - 2\right)} {\left(t - 5\right)} {y'''} + {\left(t + 5\right)} y e^{t} + e^{\left(-2 \, t\right)} \hspace{2em} x( 3 )= 8" alt="3 \, {y''} = {\left(t - 2\right)} {\left(t - 5\right)} {y'''} + {\left(t + 5\right)} y e^{t} + e^{\left(-2 \, t\right)} \hspace{2em} x( 3 )= 8" title="3 \, {y''} = {\left(t - 2\right)} {\left(t - 5\right)} {y'''} + {\left(t + 5\right)} y e^{t} + e^{\left(-2 \, t\right)} \hspace{2em} x( 3 )= 8" data-latex="3 \, {y''} = {\left(t - 2\right)} {\left(t - 5\right)} {y'''} + {\left(t + 5\right)} y e^{t} + e^{\left(-2 \, t\right)} \hspace{2em} x( 3 )= 8"/>
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  &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?3%20%5C,%20%7By''%7D%20=%20%7B%5Cleft(t%20-%202%5Cright)%7D%20%7B%5Cleft(t%20-%205%5Cright)%7D%20%7By'''%7D%20+%20%7B%5Cleft(t%20+%205%5Cright)%7D%20y%20e%5E%7Bt%7D%20+%20e%5E%7B%5Cleft(-2%20%5C,%20t%5Cright)%7D%20%5Chspace%7B2em%7D%20x(%203%20)=%208" alt="3 \, {y''} = {\left(t - 2\right)} {\left(t - 5\right)} {y'''} + {\left(t + 5\right)} y e^{t} + e^{\left(-2 \, t\right)} \hspace{2em} x( 3 )= 8" title="3 \, {y''} = {\left(t - 2\right)} {\left(t - 5\right)} {y'''} + {\left(t + 5\right)} y e^{t} + e^{\left(-2 \, t\right)} \hspace{2em} x( 3 )= 8" data-latex="3 \, {y''} = {\left(t - 2\right)} {\left(t - 5\right)} {y'''} + {\left(t + 5\right)} y e^{t} + e^{\left(-2 \, t\right)} \hspace{2em} x( 3 )= 8"&gt;
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            <h4>Partial Answer:</h4>
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              <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?(2,5)" alt="(2,5)" title="(2,5)" data-latex="(2,5)"/>
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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?(2,5)" alt="(2,5)" title="(2,5)" data-latex="(2,5)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

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