0010.qti

<item ident="N1-7248" title="N1 | Existence/uniqueness theorem for linear IVPs | ver. 7248">
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          <p>
            <strong>N1.</strong>
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          <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)} {\left(t + 1\right)} {y'} - {\left(t - 6\right)} e^{t} = {\left(t^{2} + 9\right)} {y} \hspace{2em} x( -2 )= 2" alt="-{\left(t + 5\right)} {\left(t + 1\right)} {y'} - {\left(t - 6\right)} e^{t} = {\left(t^{2} + 9\right)} {y} \hspace{2em} x( -2 )= 2" title="-{\left(t + 5\right)} {\left(t + 1\right)} {y'} - {\left(t - 6\right)} e^{t} = {\left(t^{2} + 9\right)} {y} \hspace{2em} x( -2 )= 2" data-latex="-{\left(t + 5\right)} {\left(t + 1\right)} {y'} - {\left(t - 6\right)} e^{t} = {\left(t^{2} + 9\right)} {y} \hspace{2em} x( -2 )= 2"/>
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  &lt;p&gt;
    &lt;strong&gt;N1.&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%7B%5Cleft(t%20+%201%5Cright)%7D%20%7By'%7D%20-%20%7B%5Cleft(t%20-%206%5Cright)%7D%20e%5E%7Bt%7D%20=%20%7B%5Cleft(t%5E%7B2%7D%20+%209%5Cright)%7D%20%7By%7D%20%5Chspace%7B2em%7D%20x(%20-2%20)=%202" alt="-{\left(t + 5\right)} {\left(t + 1\right)} {y'} - {\left(t - 6\right)} e^{t} = {\left(t^{2} + 9\right)} {y} \hspace{2em} x( -2 )= 2" title="-{\left(t + 5\right)} {\left(t + 1\right)} {y'} - {\left(t - 6\right)} e^{t} = {\left(t^{2} + 9\right)} {y} \hspace{2em} x( -2 )= 2" data-latex="-{\left(t + 5\right)} {\left(t + 1\right)} {y'} - {\left(t - 6\right)} e^{t} = {\left(t^{2} + 9\right)} {y} \hspace{2em} x( -2 )= 2"&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?(-5,-1)" alt="(-5,-1)" title="(-5,-1)" data-latex="(-5,-1)"/>
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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?(-5,-1)" alt="(-5,-1)" title="(-5,-1)" data-latex="(-5,-1)"&gt;
  &lt;/p&gt;
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