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<item ident="N2-9631" title="N2 | Euler's method for approximating IVP solutions | ver. 9631">
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        <div class="exercise-statement">
          <p>
            <strong>N2.</strong>
          </p>
          <p> Use Euler's method with <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?h= 0.10" alt="h= 0.10" title="h= 0.10" data-latex="h= 0.10"/> to approximate <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?x( 1.2 )" alt="x( 1.2 )" title="x( 1.2 )" data-latex="x( 1.2 )"/> and <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?y( 1.2 )" alt="y( 1.2 )" title="y( 1.2 )" data-latex="y( 1.2 )"/> given the following system of IVPs. </p>
          <p style="text-align:center;">
            <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?x'= 4 \, t^{2} x^{2} + 2 \, x y^{2} - 3 \hspace{2em} x( 1 )= 1" alt="x'= 4 \, t^{2} x^{2} + 2 \, x y^{2} - 3 \hspace{2em} x( 1 )= 1" title="x'= 4 \, t^{2} x^{2} + 2 \, x y^{2} - 3 \hspace{2em} x( 1 )= 1" data-latex="x'= 4 \, t^{2} x^{2} + 2 \, x y^{2} - 3 \hspace{2em} x( 1 )= 1"/>
          </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'= -t^{2} y - 4 \, x y - 1 \hspace{2em} y( 1 )= -1" alt="y'= -t^{2} y - 4 \, x y - 1 \hspace{2em} y( 1 )= -1" title="y'= -t^{2} y - 4 \, x y - 1 \hspace{2em} y( 1 )= -1" data-latex="y'= -t^{2} y - 4 \, x y - 1 \hspace{2em} y( 1 )= -1"/>
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      <mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;N2.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt; Use Euler's method with &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?h=%200.10" alt="h= 0.10" title="h= 0.10" data-latex="h= 0.10"&gt; to approximate &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?x(%201.2%20)" alt="x( 1.2 )" title="x( 1.2 )" data-latex="x( 1.2 )"&gt; and &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?y(%201.2%20)" alt="y( 1.2 )" title="y( 1.2 )" data-latex="y( 1.2 )"&gt; given the following system of IVPs. &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?x'=%204%20%5C,%20t%5E%7B2%7D%20x%5E%7B2%7D%20+%202%20%5C,%20x%20y%5E%7B2%7D%20-%203%20%5Chspace%7B2em%7D%20x(%201%20)=%201" alt="x'= 4 \, t^{2} x^{2} + 2 \, x y^{2} - 3 \hspace{2em} x( 1 )= 1" title="x'= 4 \, t^{2} x^{2} + 2 \, x y^{2} - 3 \hspace{2em} x( 1 )= 1" data-latex="x'= 4 \, t^{2} x^{2} + 2 \, x y^{2} - 3 \hspace{2em} x( 1 )= 1"&gt;
  &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'=%20-t%5E%7B2%7D%20y%20-%204%20%5C,%20x%20y%20-%201%20%5Chspace%7B2em%7D%20y(%201%20)=%20-1" alt="y'= -t^{2} y - 4 \, x y - 1 \hspace{2em} y( 1 )= -1" title="y'= -t^{2} y - 4 \, x y - 1 \hspace{2em} y( 1 )= -1" data-latex="y'= -t^{2} y - 4 \, x y - 1 \hspace{2em} y( 1 )= -1"&gt;
  &lt;/p&gt;
&lt;/div&gt;

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    <response_str ident="response1" rcardinality="Single">
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        <response_label ident="answer1" rshuffle="No"/>
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  <itemfeedback ident="general_fb">
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            <h4>Partial Answer:</h4>
            <ul>
              <li><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?x( 1.1 )\approx 1.30" alt="x( 1.1 )\approx 1.30" title="x( 1.1 )\approx 1.30" data-latex="x( 1.1 )\approx 1.30"/> and <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?y( 1.1 )\approx -0.600" alt="y( 1.1 )\approx -0.600" title="y( 1.1 )\approx -0.600" data-latex="y( 1.1 )\approx -0.600"/></li>
              <li><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?x( 1.2 )\approx 1.91" alt="x( 1.2 )\approx 1.91" title="x( 1.2 )\approx 1.91" data-latex="x( 1.2 )\approx 1.91"/> and <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?y( 1.2 )\approx -0.315" alt="y( 1.2 )\approx -0.315" title="y( 1.2 )\approx -0.315" data-latex="y( 1.2 )\approx -0.315"/></li>
            </ul>
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        <mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;ul&gt;
    &lt;li&gt;
&lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?x(%201.1%20)%5Capprox%201.30" alt="x( 1.1 )\approx 1.30" title="x( 1.1 )\approx 1.30" data-latex="x( 1.1 )\approx 1.30"&gt; and &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?y(%201.1%20)%5Capprox%20-0.600" alt="y( 1.1 )\approx -0.600" title="y( 1.1 )\approx -0.600" data-latex="y( 1.1 )\approx -0.600"&gt;
&lt;/li&gt;
    &lt;li&gt;
&lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?x(%201.2%20)%5Capprox%201.91" alt="x( 1.2 )\approx 1.91" title="x( 1.2 )\approx 1.91" data-latex="x( 1.2 )\approx 1.91"&gt; and &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?y(%201.2%20)%5Capprox%20-0.315" alt="y( 1.2 )\approx -0.315" title="y( 1.2 )\approx -0.315" data-latex="y( 1.2 )\approx -0.315"&gt;
&lt;/li&gt;
  &lt;/ul&gt;
&lt;/div&gt;

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