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<Text-field style="Text" layout="Normal">Maple examples for the homework, Section 2.2</Text-field>
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<Text-field style="Text" layout="Normal">First, we'll solve exercise 14 for you to use as an example in solving 9, 11, 16, and 20.  Before you go to Maple, be sure you can get the solution to the DE by hand.</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">DE14:=diff(y(x),x)=x*(x^2+1)/(4*y(x))^3;</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">#Heres the solution to the initial value problem (RHS stands for &quot;right hand side&quot;):
Y:=rhs(dsolve({DE14, y(0)=-1/2},y(x)));</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">#From the graph, it looks like our solution is defined for all x.</Text-field>
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<Text-field style="Text" layout="Normal">Here's the solution to exercise 23 (Section 2.2):</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">DE23:=diff(y(x),x)=(y(x))^2*(2+x);</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Y:=rhs(dsolve({DE23,y(0)=1},y(x)));</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot(Y,x=-5..5);</Text-field>
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<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal">NOTE:  This whole graph is NOT the solution to the IVP- Only the piece in the middle (with y(0)=1) is the solution.  That's why this function actually HAS a minimum value (otherwise, the full function does not have a minimum).</Text-field>
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<Text-field style="Text" layout="Normal"></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">dY:=simplify(diff(Y,x));</Text-field>
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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqJiwmIiIjIiIiSSJ4RzYiRiZGJiwoKiRGJ0YlRiZGJyIiJSEiI0YmRixGKw==</Equation></Text-field>
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<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal">From this, we see that the derivative is zero at x=-2, which matches with the minimizer on the graph.</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
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