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<Input>
<Text-field style="Text" layout="Normal">Example 8.8 Diffusion with Reaction</Text-field>
<Text-field style="Text" layout="Normal">Equation  (8.1.18) is solved in Maple below:</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
</Input>
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<Group labelreference="L44" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="restart:" display="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">QyhJKHJlc3RhcnRHJSpwcm90ZWN0ZWRHISIiLUkld2l0aEc2IjYjSSlpbnR0cmFuc0c2JEYkSShfc3lzbGliR0YoRiUtRic2I0kmcGxvdHNHRitGJQ==</Equation></Text-field>
</Input>
</Group>
<Group labelreference="L4" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal256">eq:=diff(u(x,t),t)=diff(u(x,t),x$2)-Phi^2*u(x,t);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJ1RzYiNiRJInhHRilJInRHRilGLCwmLUYkNiQtRiQ2JEYnRitGKyIiIiomKUkkUGhpR0YpIiIjRjJGJ0YyISIi</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L5" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal256">u(x,0):=0;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">IiIh</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L6" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc1:=u(x,t)=1;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly1JInVHNiI2JEkieEdGJUkidEdGJSIiIg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L7" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc2:=diff(u(x,t),x)=0;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJ1RzYiNiRJInhHRilJInRHRilGKyIiIQ==</Equation></Text-field>
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<Group labelreference="L8" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal256">eqs:=laplace(eq,t,s):</Text-field>
</Input>
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<Group labelreference="L9" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal256">eqs:=subs(laplace(u(x,t),t,s)=U(x),eqs);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LyomSSJzRzYiIiIiLUkiVUdGJTYjSSJ4R0YlRiYsJi1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtRi02JEYnRipGKkYmKiYpSSRQaGlHRiUiIiNGJkYnRiYhIiI=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L10" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal256">bc1:=laplace(bc1,t,s):</Text-field>
</Input>
</Group>
<Group labelreference="L11" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc1:=subs(laplace(u(x,t),t,s)=U(x),bc1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly1JIlVHNiI2I0kieEdGJSokSSJzR0YlISIi</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L12" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal256">bc2:=laplace(bc2,t,s):</Text-field>
</Input>
</Group>
<Group labelreference="L13" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc2:=subs(laplace(u(x,t),t,s)=U(x),bc2);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJVRzYiNiNJInhHRilGKyIiIQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L14" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">dsolve(eqs,U(x));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly1JIlVHNiI2I0kieEdGJSwmKiZJJF9DMUdGJSIiIi1JJHNpbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjKiYpLCZJInNHRiUhIiIqJClJJFBoaUdGJSIiI0YrRjYjRitGOkYrRidGK0YrRisqJkkkX0MyR0YlRistSSRjb3NHRi5GMUYrRis=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L15" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">U(x):=c[1]*cosh((s+Phi^2)^(1/2)*x)+c[2]*sinh((s+Phi^2)^(1/2)*x);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCYqJiZJImNHNiI2IyIiIkYoLUklY29zaEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJjYjKiYpLCZJInNHRiZGKCokKUkkUGhpR0YmIiIjRihGKCNGKEY2RihJInhHRiZGKEYoRigqJiZGJTYjRjZGKC1JJXNpbmhHRitGLkYoRig=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L16" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq0:=eval(subs(x=0,bc1)):</Text-field>
</Input>
</Group>
<Group labelreference="L17" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq1:=eval(subs(x=1,bc2)):</Text-field>
</Input>
</Group>
<Group labelreference="L18" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">con:=solve({eq0,eq1},{c[1],c[2]}):</Text-field>
</Input>
</Group>
<Group labelreference="L19" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">U(x):=subs(con,U(x));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCYqJkkic0c2IiEiIi1JJWNvc2hHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2IyomKSwmRiQiIiIqJClJJFBoaUdGJSIiI0YwRjAjRjBGNEYwSSJ4R0YlRjBGMEYwKiotSSVzaW5oR0YpNiMqJEYuRjBGMC1GKEY6RiZGJEYmLUY5RixGMEYm</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L20" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">U(x):=combine(simplify(U(x))):</Text-field>
</Input>
</Group>
<Group labelreference="L47" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The shifting theorem is used to find the inverse Laplace transform<Font superscript="true">(1)</Font><Font encoding="UTF-8"> as: L-1F(s)=exp(-\316\2462t)L=1F(s-\316\2462).</Font></Text-field>
</Input>
</Group>
<Group labelreference="L21" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">U(x):=factor(U(x));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KigtSSVjb3NoRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMqJiksJkkic0dGKCIiIiokKUkkUGhpR0YoIiIjRi5GLiNGLkYyRi4sJkkieEdGKEYuRi4hIiJGLkYuLUYkNiMqJEYrRi5GNkYtRjY=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L22" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">U1(x):=subs(s=s-Phi^2,U(x));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KigtSSVjb3NoRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMqJilJInNHRigjIiIiIiIjRi4sJkkieEdGKEYuRi4hIiJGLkYuLUYkNiMqJEYrRi5GMiwmRixGLiokKUkkUGhpR0YoRi9GLkYyRjI=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L23" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">P(s):=numer(U1(x));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQtSSVjb3NoRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMqJilJInNHRigjIiIiIiIjRi4sJkkieEdGKEYuRi4hIiJGLkYy</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L24" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Q(s):=denom(U1(x));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KiYtSSVjb3NoRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMqJClJInNHRigjIiIiIiIjRi5GLiwmRiwhIiIqJClJJFBoaUdGKEYvRi5GLkYu</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L25" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">A(s):=P(s)/diff(Q(s),s);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqJi1JJWNvc2hHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IyomKUkic0dGKSMiIiIiIiNGLywmSSJ4R0YpRi9GLyEiIkYvRi8sJioqRi5GLy1JJXNpbmhHRiY2IyokRixGL0YvRixGMywmRi1GMyokKUkkUGhpR0YpRjBGL0YvRi9GLy1GJUY4RjNGM0Yz</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L26" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">solve(Q(s),s);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">NiQsJComIyIiIiIiJUYmKUkjUGlHJSpwcm90ZWN0ZWRHIiIjRiYhIiIqJClJJFBoaUc2IkYrRiY=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L27" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">_EnvAllSolutions := true:</Text-field>
</Input>
</Group>
<Group labelreference="L28" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">solve(Q(s),s):</Text-field>
</Input>
</Group>
<Group labelreference="L48" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The roots are:</Text-field>
</Input>
</Group>
<Group labelreference="L29" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Phi^2,-((2*n-1)*Pi/2)^2;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">NiQqJClJJFBoaUc2IiIiIyIiIiwkKigjRigiIiVGKCksJiomRidGKEkibkdGJkYoRihGKCEiIkYnRigpSSNQaUclKnByb3RlY3RlZEdGJ0YoRjE=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L30" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">A[n]:=simplify(subs(s=mu,A(s)));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqKiIiIyIiIi1JJWNvc2hHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IyomKUkjbXVHRisjRiVGJEYlLCZJInhHRitGJUYlISIiRiVGJUYuRiUsKComLUklc2luaEdGKDYjKiRGLkYlRiVGL0YlRjMqJkY2RiUpSSRQaGlHRitGJEYlRiUqKEYkRiUtRidGOEYlRi5GJUYzRjNGMw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L31" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">A[0]:=subs(mu^(1/2)=Phi,mu=Phi^2,A[n]):</Text-field>
</Input>
</Group>
<Group labelreference="L32" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">A[0]:=simplify(A[0]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiQUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUkjbW5HRiQ2JFEiMEYnL0Y2USdub3JtYWxGJy8lK2ZvcmVncm91bmRHUShbMCwwLDBdRidGPi8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW9HRiQ2LVEjOj1GJ0Y+LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZMLyUpc3RyZXRjaHlHRkwvJSpzeW1tZXRyaWNHRkwvJShsYXJnZW9wR0ZMLyUubW92YWJsZWxpbWl0c0dGTC8lJ2FjY2VudEdGTC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRmVuLUkmbWZyYWNHRiQ2KC1GIzYlLUYjNictRi82JVElY29zaEYnL0YzRkxGPi1GRzYtUTAmQXBwbHlGdW5jdGlvbjtGJ0Y+RkpGTUZPRlFGU0ZVRlcvRlpRJjAuMGVtRicvRmduRmdvLUkobWZlbmNlZEdGJDYkLUYjNiUtRiM2Ji1GLzYlUScmIzkzNDtGJ0Zib0Y+LUZHNi1RMSZJbnZpc2libGVUaW1lcztGJ0Y+RkpGTUZPRlFGU0ZVRldGZm9GaG8tRmpvNiQtRiM2Ji1GLzYlUSJ4RidGMkY1LUZHNi1RKCZtaW51cztGJ0Y+RkpGTUZPRlFGU0ZVRlcvRlpRLDAuMjIyMjIyMmVtRicvRmduRmFxLUY7NiRRIjFGJ0Y+Rj5GPkY+RkBGPkY+RkBGPkZARj4tRiM2JS1GIzYnRl9vRmNvLUZqbzYkLUYjNiVGYHBGQEY+Rj5GQEY+RkBGPi8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGY3IvJSliZXZlbGxlZEdGTEZARj4=">KiYtSSVjb3NoRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMqJkkkUGhpR0YoIiIiLCZJInhHRihGLEYsISIiRixGLC1GJDYjRitGLw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L33" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">A[n]:=simplify(subs(mu^(1/2)=I*(2*n-1)/2*Pi,mu=-((2*n-1)*Pi/2)^2,A[n])):</Text-field>
</Input>
</Group>
<Group labelreference="L34" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">vars:={cos(1/2*(2*n-1)*Pi)=0,sin(1/2*(2*n-1)*Pi)=(-1)^(n-1)}:</Text-field>
</Input>
</Group>
<Group labelreference="L35" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">A[n]:=simplify(subs(vars,A[n]));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqLiIiJSIiIikhIiIsJEkibkc2IkYnRiUsJiomIiIjRiVGKUYlRiVGJUYnRiVJI1BpRyUqcHJvdGVjdGVkR0YlLUkkY29zRzYkRi9JKF9zeXNsaWJHRio2IywkKiojRiVGLUYlRitGJUYuRiUsJkkieEdGKkYlRiVGJ0YlRiVGJSwqKihGJEYlKUYuRi1GJSlGKUYtRiVGJSooRiRGJUY8RiVGKUYlRicqJEY8RiVGJSomRiRGJSlJJFBoaUdGKkYtRiVGJUYnRiU=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L36" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">u0s:=A[0]*subs(mu=Phi^2,1/(s-mu));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KigtSSVjb3NoRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMqJkkkUGhpR0YoIiIiLCZJInhHRihGLEYsISIiRixGLC1GJDYjRitGLywmSSJzR0YoRiwqJClGKyIiI0YsRi9GLw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L37" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">u0t:=invlaplace(u0s,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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">KigtSSVjb3NoRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMqJkkkUGhpR0YoIiIiLCZJInhHRihGLEYsISIiRixGLC1GJDYjRitGLy1JJGV4cEdGJTYjKiYpRisiIiNGLEkidEdGKEYsRiw=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L38" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">uns:=A[n]/(s-mu);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqMCIiJSIiIikhIiIsJEkibkc2IkYnRiUsJiomIiIjRiVGKUYlRiVGJUYnRiVJI1BpRyUqcHJvdGVjdGVkR0YlLUkkY29zRzYkRi9JKF9zeXNsaWJHRio2IywkKiojRiVGLUYlRitGJUYuRiUsJkkieEdGKkYlRiVGJ0YlRiVGJSwqKihGJEYlKUYuRi1GJSlGKUYtRiVGJSooRiRGJUY8RiVGKUYlRicqJEY8RiVGJSomRiRGJSlJJFBoaUdGKkYtRiVGJUYnLCZJInNHRipGJUkjbXVHRipGJ0YnRiU=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L39" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">unt:=invlaplace(uns,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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">LCQqMCIiJSIiIikhIiIsJEkibkc2IkYnRiUsJiomIiIjRiVGKUYlRiVGJUYnRiVJI1BpRyUqcHJvdGVjdGVkR0YlLUkkY29zRzYkRi9JKF9zeXNsaWJHRio2IywkKiojRiVGLUYlRitGJUYuRiUsJkkieEdGKkYlRiVGJ0YlRiVGJSwqKihGJEYlKUYuRi1GJSlGKUYtRiVGJSooRiRGJUY8RiVGKUYlRicqJEY8RiVGJSomRiRGJSlJJFBoaUdGKkYtRiVGJUYnLUkkZXhwR0YyNiMqJkkjbXVHRipGJUkidEdGKkYlRiVGJQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L40" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">unt:=subs(mu=-((2*n-1)/2*Pi)^2,unt);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqMCIiJSIiIikhIiIsJEkibkc2IkYnRiUsJiomIiIjRiVGKUYlRiVGJUYnRiVJI1BpRyUqcHJvdGVjdGVkR0YlLUkkY29zRzYkRi9JKF9zeXNsaWJHRio2IywkKiojRiVGLUYlRitGJUYuRiUsJkkieEdGKkYlRiVGJ0YlRiVGJSwqKihGJEYlKUYuRi1GJSlGKUYtRiVGJSooRiRGJUY8RiVGKUYlRicqJEY8RiVGJSomRiRGJSlJJFBoaUdGKkYtRiVGJUYnLUkkZXhwR0YyNiMsJCoqI0YlRiRGJSlGK0YtRiVGPEYlSSJ0R0YqRiVGJ0YlRiU=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L49" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">The time domain solution is obtained by multiplying the inverse Laplace transform of U1(x) by exp(-\316\2462t):</Font></Text-field>
</Input>
</Group>
<Group labelreference="L41" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">U:=simplify(u0t*exp(-Phi^2*t))+Sum(unt,n=1..infinity)*exp(-Phi^2*t);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCYqJi1JJWNvc2hHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IyomSSRQaGlHRikiIiIsJkkieEdGKUYtRi0hIiJGLUYtLUYlNiNGLEYwRi0qJi1JJFN1bUdGJjYkLCQqMCIiJUYtKUYwLCRJIm5HRilGMEYtLCYqJiIiI0YtRjxGLUYtRi1GMEYtSSNQaUdGJ0YtLUkkY29zR0YmNiMsJCoqI0YtRj9GLUY9Ri1GQEYtRi5GLUYtRi0sKiooRjlGLSlGQEY/Ri0pRjxGP0YtRi0qKEY5Ri1GSUYtRjxGLUYwKiRGSUYtRi0qJkY5Ri0pRixGP0YtRi1GMC1JJGV4cEdGJjYjLCQqKiNGLUY5Ri0pRj1GP0YtRklGLUkidEdGKUYtRjBGLUYtL0Y8O0YtSSlpbmZpbml0eUdGJ0YtLUZQNiMsJComRk5GLUZWRi1GMEYtRi0=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L42" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">u:=piecewise(t=0,0,t&gt;0,subs(infinity=20,U)):</Text-field>
</Input>
</Group>
<Group labelreference="L50" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The following plots are obtained:</Text-field>
</Input>
</Group>
<Group labelreference="L43" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot3d(subs(Phi=1,u),x=1..0,t=0.5..0,axes=boxed,title=&quot;Figure Exp. 8.15.&quot;,labels=[x,t,&quot;u&quot;],orientation=[-45,60]);</Text-field>
</Input>
<Output>
<Text-field style="Maple Plot" layout="Maple Plot"><Plot height="300" type="three-dimensional" width="400" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0">[encoded data, 13692 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L46" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRicvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
</Input>
</Group>
<Group labelreference="L51" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The solution obtained matches the separation of variables solution obtained in example 7.8.</Text-field>
</Input>
</Group>
</Worksheet>