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    <Task-category name="&lt;default&gt;">
    </Task-category>
</Task-table>
<Annotation-table>
    <Annotation-category name="&lt;default&gt;">
    </Annotation-category>
</Annotation-table>
<Task>
</Task>
<Group labelreference="L12" drawlabel="true">
<Input>
<Text-field style="Heading 3" italic="false" layout="Heading 3"><Font italic="false">Example 2.2.4 </Font></Text-field>
</Input>
</Group>
<Group labelreference="L11" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">restart:</Text-field>
</Input>
</Group>
<Group labelreference="L3" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">with(plots):</Text-field>
</Input>
</Group>
<Group labelreference="L13" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Enter the governing equation:</Text-field>
</Input>
</Group>
<Group labelreference="L4" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq:=diff(y(t),t$2)+2*zeta/tau*diff(y(t),t)+y(t)=1/tau^2;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjZXFHNiIvLCgtSSVkaWZmRyUqcHJvdGVjdGVkRzYkLUkieUdGJDYjSSJ0R0YkLUkiJEdGKTYkRi4iIiMiIiIqKkYyRjNJJXpldGFHRiRGM0kkdGF1R0YkISIiLUYoNiRGK0YuRjNGM0YrRjMqJClGNkYyRjc=">LywoLUklZGlmZkclKnByb3RlY3RlZEc2JC1GJTYkLUkieUc2IjYjSSJ0R0YsRi5GLiIiIioqIiIjRi9JJXpldGFHRixGL0kkdGF1R0YsISIiRihGL0YvRipGLyokKUYzRjFGNA==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L14" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Enter the parameters:</Text-field>
</Input>
</Group>
<Group labelreference="L5" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">pars:={tau=1,zeta=1/2};</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkklcGFyc0c2IjwkL0kkdGF1R0YkIiIiL0klemV0YUdGJCNGKCIiIw==">PCQvSSR0YXVHNiIiIiIvSSV6ZXRhR0YlI0YmIiIj</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L6" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq:=subs(pars,eq);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjZXFHNiIvLCgtSSVkaWZmRyUqcHJvdGVjdGVkRzYkLUkieUdGJDYjSSJ0R0YkLUkiJEdGKTYkRi4iIiMiIiItRig2JEYrRi5GM0YrRjNGMw==">LywoLUklZGlmZkclKnByb3RlY3RlZEc2JC1GJTYkLUkieUc2IjYjSSJ0R0YsRi5GLiIiIkYoRi9GKkYvRi8=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L7" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">ICs:=(y(0)=0,D(y)(0)=0);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkSUNzRzYiNiQvLUkieUdGJDYjIiIhRiovLS1JIkRHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0YoRilGKg==">NiQvLUkieUc2IjYjIiIhRigvLS1JIkRHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiY2I0YlRidGKA==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L8" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">sol:=dsolve({eq,ICs},{y(t)},type=numeric,method=gear);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L15" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Note that Gear's method is used for this example.  The following methods are available in Maple:  <Font underline="true">rkf45</Font>, <Font underline="true">rosenbrock</Font>, <Font underline="true">dverk78</Font>, <Font underline="true">1sode</Font>, <Font underline="true">gear</Font>, <Font underline="true">taylorseries</Font>, or <Font underline="true">classical</Font>.</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal">Next, the dependent variable is plotted:</Text-field>
</Input>
</Group>
<Group labelreference="L9" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">odeplot(sol,[t,y(t)],0..50,axes=boxed,title=&quot;Figure 2.2.8&quot;,thickness=4,labels=[t,&quot;y(t)&quot;]);</Text-field>
</Input>
<Output>
<Text-field style="Maple Plot" layout="Maple Plot"><Plot height="300" type="two-dimensional" width="400" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0" gridlinevisibility="1" legendvisibility="false">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</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L17" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Next, the derivative is plotted:</Text-field>
</Input>
</Group>
<Group labelreference="L10" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">odeplot(sol,[t,diff(y(t),t)],0..20,title=&quot;Figure 2.2.9&quot;,axes=boxed,thickness=4);</Text-field>
</Input>
<Output>
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