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<Text-field style="Text" bold="true" layout="Heading 3"><Font bold="true">Example 2.8 Solving Linear ODEs using Maple</Font></Text-field>
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<Text-field style="Text" layout="Normal">The reaction scheme described in example 2.1 is solved below using the 'dsolve' command.</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">restart:</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">with(plots):</Text-field>
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<Text-field style="Warning" layout="Warning">Warning, the name changecoords has been redefined
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq[1]:=diff(ca(t),t)=-k1*ca(t);</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq[2]:=diff(cb(t),t)=k1*ca(t)-k2*cb(t);</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">vars:=(ca(t),cb(t));</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eqs:=(eq[1],eq[2]);</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">ICs:=(ca(0)=1,cb(0)=0);</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">sol:=dsolve({eqs,ICs},{vars});</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">assign(sol):</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">ca(t);</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">cb(t);</Text-field>
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<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">Higher order linear ODEs can also be solved using the dsolve command.  It should be noted that Maple solves equations in symbolic form.  Therefore, even if the constants are numerical, the output is in symbolic form.  Sometimes, this output can be messy.  It should be noted that when more than two equations are solved the dsolve command may not be able to give an elegant solution.  For illustration, the heat transfer problem solved in example 2.3 is solved below using Maple\342\200\231s dsolve command.</Font></Text-field>
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