0000.qti

<item ident="S2-2012" title="S2 | Linear ODE system with elimination | ver. 2012">
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  <presentation>
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        <div class="exercise-statement">
          <p>
            <strong>S2.</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?2 \, {x} + {x'} = -3 \, {y} \hspace{2em}x(0)= 4" alt="2 \, {x} + {x'} = -3 \, {y} \hspace{2em}x(0)= 4" title="2 \, {x} + {x'} = -3 \, {y} \hspace{2em}x(0)= 4" data-latex="2 \, {x} + {x'} = -3 \, {y} \hspace{2em}x(0)= 4"/>
          </p>
          <p style="text-align:center;">
            <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?-3 \, {y} + {y'} = -12 \, {x} \hspace{2em}x(0)= 1" alt="-3 \, {y} + {y'} = -12 \, {x} \hspace{2em}x(0)= 1" title="-3 \, {y} + {y'} = -12 \, {x} \hspace{2em}x(0)= 1" data-latex="-3 \, {y} + {y'} = -12 \, {x} \hspace{2em}x(0)= 1"/>
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      <mattext texttype="text/html">&lt;div class="exercise-statement"&gt;
  &lt;p&gt;
    &lt;strong&gt;S2.&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?2%20%5C,%20%7Bx%7D%20+%20%7Bx'%7D%20=%20-3%20%5C,%20%7By%7D%20%5Chspace%7B2em%7Dx(0)=%204" alt="2 \, {x} + {x'} = -3 \, {y} \hspace{2em}x(0)= 4" title="2 \, {x} + {x'} = -3 \, {y} \hspace{2em}x(0)= 4" data-latex="2 \, {x} + {x'} = -3 \, {y} \hspace{2em}x(0)= 4"&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?-3%20%5C,%20%7By%7D%20+%20%7By'%7D%20=%20-12%20%5C,%20%7Bx%7D%20%5Chspace%7B2em%7Dx(0)=%201" alt="-3 \, {y} + {y'} = -12 \, {x} \hspace{2em}x(0)= 1" title="-3 \, {y} + {y'} = -12 \, {x} \hspace{2em}x(0)= 1" data-latex="-3 \, {y} + {y'} = -12 \, {x} \hspace{2em}x(0)= 1"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext>
    </material>
    <response_str ident="response1" rcardinality="Single">
      <render_fib>
        <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= e^{\left(7 \, t\right)} + 3 \, e^{\left(-6 \, t\right)}" alt="x= e^{\left(7 \, t\right)} + 3 \, e^{\left(-6 \, t\right)}" title="x= e^{\left(7 \, t\right)} + 3 \, e^{\left(-6 \, t\right)}" data-latex="x= e^{\left(7 \, t\right)} + 3 \, e^{\left(-6 \, 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= -3 \, e^{\left(7 \, t\right)} + 4 \, e^{\left(-6 \, t\right)}" alt="y= -3 \, e^{\left(7 \, t\right)} + 4 \, e^{\left(-6 \, t\right)}" title="y= -3 \, e^{\left(7 \, t\right)} + 4 \, e^{\left(-6 \, t\right)}" data-latex="y= -3 \, e^{\left(7 \, t\right)} + 4 \, e^{\left(-6 \, t\right)}"/>
            </p>
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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=%20e%5E%7B%5Cleft(7%20%5C,%20t%5Cright)%7D%20+%203%20%5C,%20e%5E%7B%5Cleft(-6%20%5C,%20t%5Cright)%7D" alt="x= e^{\left(7 \, t\right)} + 3 \, e^{\left(-6 \, t\right)}" title="x= e^{\left(7 \, t\right)} + 3 \, e^{\left(-6 \, t\right)}" data-latex="x= e^{\left(7 \, t\right)} + 3 \, e^{\left(-6 \, 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=%20-3%20%5C,%20e%5E%7B%5Cleft(7%20%5C,%20t%5Cright)%7D%20+%204%20%5C,%20e%5E%7B%5Cleft(-6%20%5C,%20t%5Cright)%7D" alt="y= -3 \, e^{\left(7 \, t\right)} + 4 \, e^{\left(-6 \, t\right)}" title="y= -3 \, e^{\left(7 \, t\right)} + 4 \, e^{\left(-6 \, t\right)}" data-latex="y= -3 \, e^{\left(7 \, t\right)} + 4 \, e^{\left(-6 \, t\right)}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

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