0003.qti

<item ident="S2-4709" title="S2 | Linear ODE system with elimination | ver. 4709">
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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?-4 \, {y} + {x'} = -2 \, {x} \hspace{2em}x(0)= -5" alt="-4 \, {y} + {x'} = -2 \, {x} \hspace{2em}x(0)= -5" title="-4 \, {y} + {x'} = -2 \, {x} \hspace{2em}x(0)= -5" data-latex="-4 \, {y} + {x'} = -2 \, {x} \hspace{2em}x(0)= -5"/>
          </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} - {y} = -{y'} \hspace{2em}x(0)= 0" alt="-{x} - {y} = -{y'} \hspace{2em}x(0)= 0" title="-{x} - {y} = -{y'} \hspace{2em}x(0)= 0" data-latex="-{x} - {y} = -{y'} \hspace{2em}x(0)= 0"/>
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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?-4%20%5C,%20%7By%7D%20+%20%7Bx'%7D%20=%20-2%20%5C,%20%7Bx%7D%20%5Chspace%7B2em%7Dx(0)=%20-5" alt="-4 \, {y} + {x'} = -2 \, {x} \hspace{2em}x(0)= -5" title="-4 \, {y} + {x'} = -2 \, {x} \hspace{2em}x(0)= -5" data-latex="-4 \, {y} + {x'} = -2 \, {x} \hspace{2em}x(0)= -5"&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?-%7Bx%7D%20-%20%7By%7D%20=%20-%7By'%7D%20%5Chspace%7B2em%7Dx(0)=%200" alt="-{x} - {y} = -{y'} \hspace{2em}x(0)= 0" title="-{x} - {y} = -{y'} \hspace{2em}x(0)= 0" data-latex="-{x} - {y} = -{y'} \hspace{2em}x(0)= 0"&gt;
  &lt;/p&gt;
&lt;/div&gt;

</mattext>
    </material>
    <response_str ident="response1" rcardinality="Single">
      <render_fib>
        <response_label ident="answer1" rshuffle="No"/>
      </render_fib>
    </response_str>
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  <itemfeedback ident="general_fb">
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          <div class="exercise-answer">
            <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(2 \, t\right)} - 4 \, e^{\left(-3 \, t\right)}" alt="x= -e^{\left(2 \, t\right)} - 4 \, e^{\left(-3 \, t\right)}" title="x= -e^{\left(2 \, t\right)} - 4 \, e^{\left(-3 \, t\right)}" data-latex="x= -e^{\left(2 \, t\right)} - 4 \, 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)}"/>
            </p>
          </div>
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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=%20-e%5E%7B%5Cleft(2%20%5C,%20t%5Cright)%7D%20-%204%20%5C,%20e%5E%7B%5Cleft(-3%20%5C,%20t%5Cright)%7D" alt="x= -e^{\left(2 \, t\right)} - 4 \, e^{\left(-3 \, t\right)}" title="x= -e^{\left(2 \, t\right)} - 4 \, e^{\left(-3 \, t\right)}" data-latex="x= -e^{\left(2 \, t\right)} - 4 \, 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=%20-e%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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</item>