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<item ident="N2-3803" title="N2 | Euler's method for approximating IVP solutions | ver. 3803">
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          <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 x^{2} + 4 \, t y^{2} - 2 \hspace{2em} x( 1 )= -1" alt="x'= -4 \, t x^{2} + 4 \, t y^{2} - 2 \hspace{2em} x( 1 )= -1" title="x'= -4 \, t x^{2} + 4 \, t y^{2} - 2 \hspace{2em} x( 1 )= -1" data-latex="x'= -4 \, t x^{2} + 4 \, t y^{2} - 2 \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^{2} + 3 \, t x \hspace{2em} y( 1 )= 2" alt="y'= t^{2} y^{2} + 3 \, t x \hspace{2em} y( 1 )= 2" title="y'= t^{2} y^{2} + 3 \, t x \hspace{2em} y( 1 )= 2" data-latex="y'= t^{2} y^{2} + 3 \, t x \hspace{2em} y( 1 )= 2"/>
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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'=%20-4%20%5C,%20t%20x%5E%7B2%7D%20+%204%20%5C,%20t%20y%5E%7B2%7D%20-%202%20%5Chspace%7B2em%7D%20x(%201%20)=%20-1" alt="x'= -4 \, t x^{2} + 4 \, t y^{2} - 2 \hspace{2em} x( 1 )= -1" title="x'= -4 \, t x^{2} + 4 \, t y^{2} - 2 \hspace{2em} x( 1 )= -1" data-latex="x'= -4 \, t x^{2} + 4 \, t y^{2} - 2 \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'=%20t%5E%7B2%7D%20y%5E%7B2%7D%20+%203%20%5C,%20t%20x%20%5Chspace%7B2em%7D%20y(%201%20)=%202" alt="y'= t^{2} y^{2} + 3 \, t x \hspace{2em} y( 1 )= 2" title="y'= t^{2} y^{2} + 3 \, t x \hspace{2em} y( 1 )= 2" data-latex="y'= t^{2} y^{2} + 3 \, t x \hspace{2em} y( 1 )= 2"&gt;
  &lt;/p&gt;
&lt;/div&gt;

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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 0.000" alt="x( 1.1 )\approx 0.000" title="x( 1.1 )\approx 0.000" data-latex="x( 1.1 )\approx 0.000"/> and <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?y( 1.1 )\approx 2.10" alt="y( 1.1 )\approx 2.10" title="y( 1.1 )\approx 2.10" data-latex="y( 1.1 )\approx 2.10"/></li>
              <li><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?x( 1.2 )\approx 1.74" alt="x( 1.2 )\approx 1.74" title="x( 1.2 )\approx 1.74" data-latex="x( 1.2 )\approx 1.74"/> and <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?y( 1.2 )\approx 2.63" alt="y( 1.2 )\approx 2.63" title="y( 1.2 )\approx 2.63" data-latex="y( 1.2 )\approx 2.63"/></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%200.000" alt="x( 1.1 )\approx 0.000" title="x( 1.1 )\approx 0.000" data-latex="x( 1.1 )\approx 0.000"&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%202.10" alt="y( 1.1 )\approx 2.10" title="y( 1.1 )\approx 2.10" data-latex="y( 1.1 )\approx 2.10"&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%201.74" alt="x( 1.2 )\approx 1.74" title="x( 1.2 )\approx 1.74" data-latex="x( 1.2 )\approx 1.74"&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%202.63" alt="y( 1.2 )\approx 2.63" title="y( 1.2 )\approx 2.63" data-latex="y( 1.2 )\approx 2.63"&gt;
&lt;/li&gt;
  &lt;/ul&gt;
&lt;/div&gt;

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