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<quiz>
  <question type="multichoice">
    <name>
      <text>19.1.2.2 Solution of a Differential Equation</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p class="HELM_exercise">Exercise</p>
Which of the following differential equations is satisfied by \(y=A\cosh
2x+B\sinh 2x\) where \(A\) and \(B\) are arbitrary constants.]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text><![CDATA[<p>We are given\(y=A\cosh 2x+B\sinh 2x\) where \(A\) and \(B\) are arbitrary constants.</p>
<p>Differentiating once we obtain \[{dy\over dx}=2A\sinh 2x +2B\cosh 2x.\]Differentiating a second time we obtain \[{d^2y\over {dx^2}}=4A\cosh 2x +4B\sinh 2x.\] Hence \[ {d^2y\over {dx^2}}=4y\]</p>]]></text>
    </generalfeedback>
    <defaultgrade>1</defaultgrade>
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    <single>true</single>
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    <answernumbering>abc</answernumbering>
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    <correctfeedback format="html">
      <text>Your answer is correct.</text>
    </correctfeedback>
    <partiallycorrectfeedback format="html">
      <text>Your answer is partially correct.</text>
    </partiallycorrectfeedback>
    <incorrectfeedback format="html">
      <text>Your answer is incorrect.</text>
    </incorrectfeedback>
    <shownumcorrect/>
    <answer fraction="100" format="html">
      <text><![CDATA[<p dir="ltr" style="text-align: left;">\(\dfrac{d^2y}{dx^2} = 4y\)</p>]]></text>
      <feedback format="html">
        <text/>
      </feedback>
    </answer>
    <answer fraction="0" format="html">
      <text><![CDATA[<p dir="ltr" style="text-align: left;">\(\dfrac{d^2y}{dx^2} = 3y\)<br></p>]]></text>
      <feedback format="html">
        <text/>
      </feedback>
    </answer>
    <answer fraction="0" format="html">
      <text><![CDATA[<p dir="ltr" style="text-align: left;">\(\dfrac{d^2y}{dx^2} = 4y^2\)<br></p>]]></text>
      <feedback format="html">
        <text/>
      </feedback>
    </answer>
    <answer fraction="0" format="html">
      <text><![CDATA[<p dir="ltr" style="text-align: left;">\(\dfrac{d^2y}{dx^2} = 2y\)<br></p>]]></text>
      <feedback format="html">
        <text/>
      </feedback>
    </answer>
  </question>
</quiz>
