0003.qti

<item ident="X1-9721" title="X1 | Linear ODE systems | ver. 9721">
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          <p>
            <strong>X1.</strong>
          </p>
          <p>Find the solution to the given 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'} - {x} - 4 \, {y} = 0 \hspace{2em}x(0)= 3" alt="{x'} - {x} - 4 \, {y} = 0 \hspace{2em}x(0)= 3" title="{x'} - {x} - 4 \, {y} = 0 \hspace{2em}x(0)= 3" data-latex="{x'} - {x} - 4 \, {y} = 0 \hspace{2em}x(0)= 3"/>
          </p>
          <p style="text-align:center;">
            <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?2 \, {y} = {x} - {y'} \hspace{2em}x(0)= 2" alt="2 \, {y} = {x} - {y'} \hspace{2em}x(0)= 2" title="2 \, {y} = {x} - {y'} \hspace{2em}x(0)= 2" data-latex="2 \, {y} = {x} - {y'} \hspace{2em}x(0)= 2"/>
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      <mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;X1.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Find the solution to the given 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?%7Bx'%7D%20-%20%7Bx%7D%20-%204%20%5C,%20%7By%7D%20=%200%20%5Chspace%7B2em%7Dx(0)=%203" alt="{x'} - {x} - 4 \, {y} = 0 \hspace{2em}x(0)= 3" title="{x'} - {x} - 4 \, {y} = 0 \hspace{2em}x(0)= 3" data-latex="{x'} - {x} - 4 \, {y} = 0 \hspace{2em}x(0)= 3"&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?2%20%5C,%20%7By%7D%20=%20%7Bx%7D%20-%20%7By'%7D%20%5Chspace%7B2em%7Dx(0)=%202" alt="2 \, {y} = {x} - {y'} \hspace{2em}x(0)= 2" title="2 \, {y} = {x} - {y'} \hspace{2em}x(0)= 2" data-latex="2 \, {y} = {x} - {y'} \hspace{2em}x(0)= 2"&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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            <h4>Partial Answer:</h4>
            <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 \, e^{\left(2 \, t\right)} - e^{\left(-3 \, t\right)}" alt="x= 4 \, e^{\left(2 \, t\right)} - e^{\left(-3 \, t\right)}" title="x= 4 \, e^{\left(2 \, t\right)} - e^{\left(-3 \, t\right)}" data-latex="x= 4 \, e^{\left(2 \, t\right)} - e^{\left(-3 \, t\right)}"/>
            </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= e^{\left(2 \, t\right)} + e^{\left(-3 \, t\right)}" alt="y= e^{\left(2 \, t\right)} + e^{\left(-3 \, t\right)}" title="y= e^{\left(2 \, t\right)} + e^{\left(-3 \, t\right)}" data-latex="y= e^{\left(2 \, t\right)} + e^{\left(-3 \, t\right)}"/>
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        <mattext texttype="text/html">&lt;div class="exercise-answer"&gt;
  &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?x=%204%20%5C,%20e%5E%7B%5Cleft(2%20%5C,%20t%5Cright)%7D%20-%20e%5E%7B%5Cleft(-3%20%5C,%20t%5Cright)%7D" alt="x= 4 \, e^{\left(2 \, t\right)} - e^{\left(-3 \, t\right)}" title="x= 4 \, e^{\left(2 \, t\right)} - e^{\left(-3 \, t\right)}" data-latex="x= 4 \, e^{\left(2 \, t\right)} - e^{\left(-3 \, t\right)}"&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=%20e%5E%7B%5Cleft(2%20%5C,%20t%5Cright)%7D%20+%20e%5E%7B%5Cleft(-3%20%5C,%20t%5Cright)%7D" alt="y= e^{\left(2 \, t\right)} + e^{\left(-3 \, t\right)}" title="y= e^{\left(2 \, t\right)} + e^{\left(-3 \, t\right)}" data-latex="y= e^{\left(2 \, t\right)} + e^{\left(-3 \, t\right)}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

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