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<item ident="N2-4689" title="N2 | Euler's method for approximating IVP solutions | ver. 4689">
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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( -1.8 )" alt="x( -1.8 )" title="x( -1.8 )" data-latex="x( -1.8 )"/> and <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?y( -1.8 )" alt="y( -1.8 )" title="y( -1.8 )" data-latex="y( -1.8 )"/> 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'= t^{2} x - 3 \, t^{2} y + 3 \hspace{2em} x( -2 )= 1" alt="x'= t^{2} x - 3 \, t^{2} y + 3 \hspace{2em} x( -2 )= 1" title="x'= t^{2} x - 3 \, t^{2} y + 3 \hspace{2em} x( -2 )= 1" data-latex="x'= t^{2} x - 3 \, t^{2} y + 3 \hspace{2em} x( -2 )= 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'= -x y^{2} + 2 \, t x - 2 \hspace{2em} y( -2 )= -1" alt="y'= -x y^{2} + 2 \, t x - 2 \hspace{2em} y( -2 )= -1" title="y'= -x y^{2} + 2 \, t x - 2 \hspace{2em} y( -2 )= -1" data-latex="y'= -x y^{2} + 2 \, t x - 2 \hspace{2em} y( -2 )= -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(%20-1.8%20)" alt="x( -1.8 )" title="x( -1.8 )" data-latex="x( -1.8 )"&gt; and &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?y(%20-1.8%20)" alt="y( -1.8 )" title="y( -1.8 )" data-latex="y( -1.8 )"&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'=%20t%5E%7B2%7D%20x%20-%203%20%5C,%20t%5E%7B2%7D%20y%20+%203%20%5Chspace%7B2em%7D%20x(%20-2%20)=%201" alt="x'= t^{2} x - 3 \, t^{2} y + 3 \hspace{2em} x( -2 )= 1" title="x'= t^{2} x - 3 \, t^{2} y + 3 \hspace{2em} x( -2 )= 1" data-latex="x'= t^{2} x - 3 \, t^{2} y + 3 \hspace{2em} x( -2 )= 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-x%20y%5E%7B2%7D%20+%202%20%5C,%20t%20x%20-%202%20%5Chspace%7B2em%7D%20y(%20-2%20)=%20-1" alt="y'= -x y^{2} + 2 \, t x - 2 \hspace{2em} y( -2 )= -1" title="y'= -x y^{2} + 2 \, t x - 2 \hspace{2em} y( -2 )= -1" data-latex="y'= -x y^{2} + 2 \, t x - 2 \hspace{2em} y( -2 )= -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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          <div class="exercise-answer">
            <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( -1.9 )\approx 2.90" alt="x( -1.9 )\approx 2.90" title="x( -1.9 )\approx 2.90" data-latex="x( -1.9 )\approx 2.90"/> and <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?y( -1.9 )\approx -1.70" alt="y( -1.9 )\approx -1.70" title="y( -1.9 )\approx -1.70" data-latex="y( -1.9 )\approx -1.70"/></li>
              <li><img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?x( -1.8 )\approx 6.09" alt="x( -1.8 )\approx 6.09" title="x( -1.8 )\approx 6.09" data-latex="x( -1.8 )\approx 6.09"/> and <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?y( -1.8 )\approx -3.84" alt="y( -1.8 )\approx -3.84" title="y( -1.8 )\approx -3.84" data-latex="y( -1.8 )\approx -3.84"/></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(%20-1.9%20)%5Capprox%202.90" alt="x( -1.9 )\approx 2.90" title="x( -1.9 )\approx 2.90" data-latex="x( -1.9 )\approx 2.90"&gt; and &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?y(%20-1.9%20)%5Capprox%20-1.70" alt="y( -1.9 )\approx -1.70" title="y( -1.9 )\approx -1.70" data-latex="y( -1.9 )\approx -1.70"&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(%20-1.8%20)%5Capprox%206.09" alt="x( -1.8 )\approx 6.09" title="x( -1.8 )\approx 6.09" data-latex="x( -1.8 )\approx 6.09"&gt; and &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?y(%20-1.8%20)%5Capprox%20-3.84" alt="y( -1.8 )\approx -3.84" title="y( -1.8 )\approx -3.84" data-latex="y( -1.8 )\approx -3.84"&gt;
&lt;/li&gt;
  &lt;/ul&gt;
&lt;/div&gt;

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