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      <text>19.1.3.2 Example on classifying differential equations</text>
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      <text><![CDATA[<h4 class="HELM_example">Example</h4>
<p>Classify the differential equations specifying the order and type (linear/non-linear) </p>
<ol class="HELM_parts">
    <li><span class="math inline">\(\displaystyle{{d^2y\over dx^2}-{dy\over dx}=x^2}\)</span></li>
    <li><span class="math inline">\(\displaystyle{{d^2x\over dt^2}=\left({dx\over dt}\right)^3+3x}\)</span></li>
    <li><span class="math inline">\(\displaystyle{{dx\over dt}-x=t^2}\)</span></li>
    <li><span class="math inline">\(\displaystyle{{dy\over dt}+\cos y=0}\)</span></li>
    <li><span class="math inline">\(\displaystyle{{dy\over dt}+y^2=4}\)</span></li>
</ol>



<h4 class="HELM_solution">Solution</h4>
<ol class="HELM_parts">
    <li>Second order, linear</li>
    <li>Second order, non-linear (because of the cubic term).</li>
    <li>First order, linear.</li>
    <li>First order, non-linear (because of the \(\cos y\) term)</li>
    <li> First order, non-linear (because of the \(y^2\) term).</li>
</ol>
<p>Note that in (a) the independent variable is \(x\) whereas in the other cases it is \(t\). In (a), (d) and (e) the dependent variable is \(y\) and in (b) and (c) it is \(x\).</p>]]></text>
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