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    <name>
      <text>19.2.2.5 Separation of Variables Ex3</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p class="HELM_exercise">Exercise</p>
<p>Find the general solution of the following equations:
</p><ol class="HELM_parts">
  <li><p>\(\dfrac{\mathrm{d}y}{\mathrm{d}x} = {@a1@}\).</p>
    <p>\(y =\) [[input:ans1]] [[validation:ans1]] \( + C\) [[feedback:prt1]]</p></li>
     
  <li><p>\(\dfrac{\mathrm{d}y}{\mathrm{d}x} = \displaystyle{@f2@}\).</p>
    <p>\(\dfrac{1}{2}y^2 =\) [[input:ans2]] [[validation:ans2]] \( + C\) [[feedback:prt2]]</p></li>
</ol>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text><![CDATA[<ol class="HELM_parts">
  <li><p>We are given the equation \(\dfrac{\mathrm{d}y}{\mathrm{d}x} = {@a1@}\).</p>
    <p>Rearranging this equation to obtain two integrals gives \(\displaystyle\int 1 \ \mathrm{d}y = \displaystyle\int {@a1@} \ \mathrm{d}x\).</p>
    <p>Integrating gives \(y = {@a1@}x + C\).</p></li>
  
  <li><p>We are given the equation \(\dfrac{\mathrm{d}y}{\mathrm{d}x} = \displaystyle{@f2@}\). </p>
    <p>Rearranging this equation to obtain two integrals gives \(\displaystyle\int y \ \mathrm{d}y = \displaystyle\int {@a2*sin(x)@} \ \mathrm{d}x\).</p>
    <p>Integrating gives \(\dfrac{1}{2}y^2 = {@ta2@} + C\).</p></li>
    
    
</ol>]]></text>
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    <stackversion>
      <text>2020120600</text>
    </stackversion>
    <questionvariables>
      <text>a1: 2+rand(5);
a2: 4+rand(5);

f2: a2*sin(x)/y

ta1: a1*x
ta2: int(a2*sin(x),x)</text>
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    <questionnote format="moodle_auto_format">
      <text>\(\dfrac{\mathrm{d}y}{\mathrm{d}x} = {@a1@}, y = {@ta1@}, \quad  \dfrac{\mathrm{d}y}{\mathrm{d}x} = \displaystyle{@f2@}, \dfrac{1}{2}y^2 = {@ta2@} \)</text>
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      <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Your answer is partially correct.]]></text>
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