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<Input>
<Text-field style="Heading 3" italic="false" layout="Heading 3"><Font italic="false">Example 2.6 Laplace Solution of Example 2.1 Equations</Font></Text-field>
</Input>
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<Group labelreference="L30" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The initial value problem solved in example 2.1 is solved below using the Laplace transform technique following the procedure described above.</Text-field>
</Input>
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<Group labelreference="L24" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">restart:</Text-field>
</Input>
</Group>
<Group labelreference="L4" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">with(linalg):with(plots):</Text-field>
</Input>
<Output>
<Text-field style="Warning" layout="Warning">Warning, the protected names norm and trace have been redefined and unprotected
</Text-field>
<Text-field style="Warning" layout="Warning">Warning, the name changecoords has been redefined
</Text-field>
</Output>
</Group>
<Group labelreference="L5" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">with(inttrans):</Text-field>
</Input>
<Output>
<Text-field style="Warning" layout="Warning">Warning, the name hilbert has been redefined
</Text-field>
</Output>
</Group>
<Group labelreference="L6" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq[1]:=diff(ca(t),t)=-k1*ca(t);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiM+JiUjZXFHNiMiIiIvLSUlZGlmZkc2JC0lI2NhRzYjJSJ0RyUidEcsJComJSNrMUciIiItJSNjYUc2IyUidEciIiIhIiI=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L7" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq[2]:=diff(cb(t),t)=k1*ca(t)-k2*cb(t);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiM+JiUjZXFHNiMiIiMvLSUlZGlmZkc2JC0lI2NiRzYjJSJ0RyUidEcsJiomJSNrMUciIiItJSNjYUc2IyUidEciIiIiIiIqJiUjazJHIiIiLSUjY2JHNiMlInRHIiIiISIi</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L8" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=2;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiM+JSJORyIiIw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L9" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">ca(0):=1;cb(0):=0;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiM+LSUjY2FHNiMiIiEiIiI=</Equation></Text-field>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiM+LSUjY2JHNiMiIiEiIiE=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L10" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq[1]:=laplace(eq[1],t,s);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiM+JiUjZXFHNiMiIiIvLCYqJiUic0ciIiItJShsYXBsYWNlRzYlLSUjY2FHNiMlInRHJSJ0RyUic0ciIiIiIiIiIiIhIiIsJComJSNrMUciIiItJShsYXBsYWNlRzYlLSUjY2FHNiMlInRHJSJ0RyUic0ciIiIhIiI=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L11" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq[2]:=laplace(eq[2],t,s);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiM+JiUjZXFHNiMiIiMvKiYlInNHIiIiLSUobGFwbGFjZUc2JS0lI2NiRzYjJSJ0RyUidEclInNHIiIiLCYqJiUjazFHIiIiLSUobGFwbGFjZUc2JS0lI2NhRzYjJSJ0RyUidEclInNHIiIiIiIiKiYlI2syRyIiIi0lKGxhcGxhY2VHNiUtJSNjYkc2IyUidEclInRHJSJzRyIiIiEiIg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L12" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eqs:=[eq[1],eq[2]];</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output12"><Equation executable="false" style="2D Output">NiM+JSRlcXNHNyQvLCYqJiUic0ciIiItJShsYXBsYWNlRzYlLSUjY2FHNiMlInRHJSJ0RyUic0ciIiIiIiIiIiIhIiIsJComJSNrMUciIiItJShsYXBsYWNlRzYlLSUjY2FHNiMlInRHJSJ0RyUic0ciIiIhIiIvKiYlInNHIiIiLSUobGFwbGFjZUc2JS0lI2NiRzYjJSJ0RyUidEclInNHIiIiLCYqJiUjazFHIiIiLSUobGFwbGFjZUc2JS0lI2NhRzYjJSJ0RyUidEclInNHIiIiIiIiKiYlI2syRyIiIi0lKGxhcGxhY2VHNiUtJSNjYkc2IyUidEclInRHJSJzRyIiIiEiIg==</Equation></Text-field>
</Output>
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<Group labelreference="L26" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Dummy variables are introduced for convenience.</Text-field>
</Input>
</Group>
<Group labelreference="L13" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">dummyvar:={laplace(ca(t),t,s)=ua,laplace(cb(t),t,s)=ub};</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiM+JSlkdW1teXZhckc8JC8tJShsYXBsYWNlRzYlLSUjY2FHNiMlInRHJSJ0RyUic0clI3VhRy8tJShsYXBsYWNlRzYlLSUjY2JHNiMlInRHJSJ0RyUic0clI3ViRw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L14" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eqs:=subs(dummyvar,eqs);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiM+JSRlcXNHNyQvLCYqJiUic0ciIiIlI3VhRyIiIiIiIiIiIiEiIiwkKiYlI2sxRyIiIiUjdWFHIiIiISIiLyomJSJzRyIiIiUjdWJHIiIiLCYqJiUjazFHIiIiJSN1YUciIiIiIiIqJiUjazJHIiIiJSN1YkciIiIhIiI=</Equation></Text-field>
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</Group>
<Group labelreference="L15" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">vars:=[ua,ub];</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiM+JSV2YXJzRzckJSN1YUclI3ViRw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L16" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">P:=genmatrix(eqs,vars,'B');</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>
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<Group labelreference="L17" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">b:=matrix(N,1):for i to N do b[i,1]:=B[i]:od:evalm(b);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkobWZlbmNlZEdGJDYmLUYjNiUtSSdtdGFibGVHRiQ2Ni1JJG10ckdGJDYmLUkkbXRkR0YkNigtSSNtbkdGJDYkUSIxRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUpcm93YWxpZ25HUSFGJy8lLGNvbHVtbmFsaWduR0ZCLyUrZ3JvdXBhbGlnbkdGQi8lKHJvd3NwYW5HUSIxRicvJStjb2x1bW5zcGFuR0ZJRkBGQ0ZFLUY0NiYtRjc2KC1GOjYkUSIwRidGPUZARkNGRUZHRkpGQEZDRkUvJSZhbGlnbkdRJWF4aXNGJy9GQVEpYmFzZWxpbmVGJy9GRFEmcmlnaHRGJy9GRlEnfGZybGVmdHxockYnLyUvYWxpZ25tZW50c2NvcGVHUSV0cnVlRicvJSxjb2x1bW53aWR0aEdRJWF1dG9GJy8lJndpZHRoR0Zbby8lK3Jvd3NwYWNpbmdHUSYxLjBleEYnLyUuY29sdW1uc3BhY2luZ0dRJjAuOGVtRicvJSlyb3dsaW5lc0dRJW5vbmVGJy8lLGNvbHVtbmxpbmVzR0Zmby8lJmZyYW1lR0Zmby8lLWZyYW1lc3BhY2luZ0dRLDAuNGVtfjAuNWV4RicvJSplcXVhbHJvd3NHUSZmYWxzZUYnLyUtZXF1YWxjb2x1bW5zR0ZgcC8lLWRpc3BsYXlzdHlsZUdGYHAvJSVzaWRlR0ZZLyUwbWlubGFiZWxzcGFjaW5nR0Zjby8lK2ZvcmVncm91bmRHUShbMCwwLDBdRidGPUY9LyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnRmlwRj0=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L18" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">sol:=evalm(inverse(P)&amp;*b);</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="L27" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The vector 'sol' is the solution in the Laplace domain.   This is converted to the time domain by using Maple's 'map' command with the 'invlaplace' command.</Text-field>
</Input>
</Group>
<Group labelreference="L19" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">solt:=map(invlaplace,sol,s,t);</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="L20" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">ca:=solt[1,1];</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiM+JSNjYUctJSRleHBHNiMsJComJSNrMUciIiIlInRHIiIiISIi</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L21" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">cb:=solt[2,1];</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiM+JSNjYkcqKCUjazFHIiIiLCYtJSRleHBHNiMsJComJSNrMUciIiIlInRHIiIiISIiISIiLSUkZXhwRzYjLCQqJiUjazJHIiIiJSJ0RyIiIiEiIiIiIiIiIiwmJSNrMUciIiIlI2syRyEiIiEiIg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L22" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">cc:=1-ca-cb;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiM+JSNjY0csKCIiIiIiIi0lJGV4cEc2IywkKiYlI2sxRyIiIiUidEciIiIhIiIhIiIqKCUjazFHIiIiLCYtJSRleHBHNiMsJComJSNrMUciIiIlInRHIiIiISIiISIiLSUkZXhwRzYjLCQqJiUjazJHIiIiJSJ0RyIiIiEiIiIiIiIiIiwmJSNrMUciIiIlI2syRyEiIiEiIiEiIg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L28" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">These results are consistent with those presented in Example 2.1.</Text-field>
</Input>
</Group>
<Group labelreference="L23" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
</Worksheet>