<?xml version="1.0" encoding="UTF-8"?>
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<Page-Numbers enabled="false" first-number="1" first-numbered-page="1" horizontal-location="right" style="Page Number" vertical-location="bottom"/>
<Task-table>
    <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="L52" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Example 7.12 Diffusion in a Cylinder</Text-field>
</Input>
</Group>
<Group labelreference="L51" 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="L4" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq:=diff(u(x,y),y$2)=-diff(u(x,y),x$2)-1/x*diff(u(x,y),x);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjZXFHNiIvLUklZGlmZkclKnByb3RlY3RlZEc2JC1JInVHRiQ2JEkieEdGJEkieUdGJC1JIiRHRig2JEYuIiIjLCYtRic2JEYqLUYwNiRGLUYyISIiKiZGLUY4LUYnNiRGKkYtIiIiRjg=">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtRiQ2JC1JInVHNiI2JEkieEdGK0kieUdGK0YuRi4sJi1GJDYkLUYkNiRGKUYtRi0hIiIqJkYtRjRGMiIiIkY0</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L5" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc1:=diff(u(x,y),x)=0;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMxRzYiLy1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJ1R0YkNiRJInhHRiRJInlHRiRGLSIiIQ==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJ1RzYiNiRJInhHRilJInlHRilGKyIiIQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L6" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc2:=u(x,y)=0;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMyRzYiLy1JInVHRiQ2JEkieEdGJEkieUdGJCIiIQ==">Ly1JInVHNiI2JEkieEdGJUkieUdGJSIiIQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L7" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc3:=u(x,y)=1;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMzRzYiLy1JInVHRiQ2JEkieEdGJEkieUdGJCIiIg==">Ly1JInVHNiI2JEkieEdGJUkieUdGJSIiIg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L8" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc4:=diff(u(x,y),x)=0;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmM0RzYiLy1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJ1R0YkNiRJInhHRiRJInlHRiRGLSIiIQ==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJ1RzYiNiRJInhHRilJInlHRilGKyIiIQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L9" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Eq:=subs(u(x,y)=X(x)*Y(y),eq);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjRXFHNiIvLUklZGlmZkclKnByb3RlY3RlZEc2JComLUkiWEdGJDYjSSJ4R0YkIiIiLUkiWUdGJDYjSSJ5R0YkRi8tSSIkR0YoNiRGMyIiIywmLUYnNiRGKi1GNTYkRi5GNyEiIiomRi5GPS1GJzYkRipGLkYvRj0=">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtRiQ2JComLUkiWEc2IjYjSSJ4R0YsIiIiLUkiWUdGLDYjSSJ5R0YsRi9GM0YzLCYtRiQ2JC1GJDYkRilGLkYuISIiKiZGLkY5RjdGL0Y5</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L10" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Eq:=expand(Eq/X(x)/Y(y));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjRXFHNiIvKiYtSSJZR0YkNiNJInlHRiQhIiItSSVkaWZmRyUqcHJvdGVjdGVkRzYkRictSSIkR0YuNiRGKiIiIyIiIiwmKiYtSSJYR0YkNiNJInhHRiRGKy1GLTYkRjctRjE2JEY6RjNGNEYrKihGN0YrRjpGKy1GLTYkRjdGOkY0Ris=">LyomLUkiWUc2IjYjSSJ5R0YmISIiLUklZGlmZkclKnByb3RlY3RlZEc2JC1GKzYkRiRGKEYoIiIiLCYqJi1JIlhHRiY2I0kieEdGJkYpLUYrNiQtRis2JEYzRjZGNkYwRikqKEYzRilGNkYpRjlGMEYp</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L11" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Eq_Y:=lhs(Eq)=lambda^2:</Text-field>
</Input>
</Group>
<Group labelreference="L12" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Eq_Y:=eval(Eq_Y*Y(y));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkklRXFfWUc2Ii8tSSVkaWZmRyUqcHJvdGVjdGVkRzYkLUkiWUdGJDYjSSJ5R0YkLUkiJEdGKDYkRi0iIiMqJkYqIiIiKUknbGFtYmRhR0YkRjFGMw==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtRiQ2JC1JIllHNiI2I0kieUdGK0YtRi0qJkYpIiIiSSdsYW1iZGFHRisiIiM=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L13" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">dsolve(Eq_Y,Y(y));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly1JIllHNiI2I0kieUdGJSwmKiZJJF9DMUdGJSIiIi1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjLCQqJkknbGFtYmRhR0YlRitGJ0YrISIiRitGKyomSSRfQzJHRiVGKy1GLTYjRjNGK0Yr</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L14" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Y(y):=C[1]*sinh(lambda*y)+C[2]*cosh(lambda*y);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pi1JIllHNiI2I0kieUdGJSwmKiYmSSJDR0YlNiMiIiJGLS1JJXNpbmhHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2IyomSSdsYW1iZGFHRiVGLUYnRi1GLUYtKiYmRis2IyIiI0YtLUklY29zaEdGMEYzRi1GLQ==">LCYqJiZJIkNHNiI2IyIiIkYoLUklc2luaEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJjYjKiZJJ2xhbWJkYUdGJkYoSSJ5R0YmRihGKEYoKiYmRiU2IyIiI0YoLUklY29zaEdGK0YuRihGKA==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L15" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Bc4:=diff(Y(y),y)=0;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkQmM0RzYiLywmKigmSSJDR0YkNiMiIiJGKy1JJWNvc2hHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2IyomSSdsYW1iZGFHRiRGK0kieUdGJEYrRitGM0YrRisqKCZGKTYjIiIjRistSSVzaW5oR0YuRjFGK0YzRitGKyIiIQ==">LywmKigmSSJDRzYiNiMiIiJGKS1JJWNvc2hHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRic2IyomSSdsYW1iZGFHRidGKUkieUdGJ0YpRilGMUYpRikqKCZGJjYjIiIjRiktSSVzaW5oR0YsRi9GKUYxRilGKSIiIQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L16" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Eq_Bc4:=eval(subs(y=1,Bc4));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkknRXFfQmM0RzYiLywmKigmSSJDR0YkNiMiIiJGKy1JJWNvc2hHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0knbGFtYmRhR0YkRitGMkYrRisqKCZGKTYjIiIjRistSSVzaW5oR0YuRjFGK0YyRitGKyIiIQ==">LywmKigmSSJDRzYiNiMiIiJGKS1JJWNvc2hHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRic2I0knbGFtYmRhR0YnRilGMEYpRikqKCZGJjYjIiIjRiktSSVzaW5oR0YsRi9GKUYwRilGKSIiIQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L17" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">C[2]:=solve(Eq_Bc4,C[2]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJIkNHNiI2IyIiIywkKigmRiQ2IyIiIkYsLUklY29zaEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjSSdsYW1iZGFHRiVGLC1JJXNpbmhHRi9GMiEiIkY2">LCQqKCZJIkNHNiI2IyIiIkYoLUklY29zaEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJjYjSSdsYW1iZGFHRiZGKC1JJXNpbmhHRitGLiEiIkYy</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L18" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Y(y):=eval(Y(y));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pi1JIllHNiI2I0kieUdGJSwmKiYmSSJDR0YlNiMiIiJGLS1JJXNpbmhHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2IyomSSdsYW1iZGFHRiVGLUYnRi1GLUYtKipGKkYtLUklY29zaEdGMDYjRjVGLS1GL0Y5ISIiLUY4RjNGLUY7">LCYqJiZJIkNHNiI2IyIiIkYoLUklc2luaEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJjYjKiZJJ2xhbWJkYUdGJkYoSSJ5R0YmRihGKEYoKipGJEYoLUklY29zaEdGKzYjRjBGKC1GKkY1ISIiLUY0Ri5GKEY3</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L19" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">combine(Y(y));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LVEqJnVtaW51czA7RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRkMtSSZtZnJhY0dGJDYoLUYjNictSSVtc3ViR0YkNiUtSSNtaUdGJDYlUSJDRicvJSdpdGFsaWNHUSV0cnVlRicvRjBRJ2l0YWxpY0YnLUYjNiUtSSNtbkdGJDYkUSIxRidGLy8lK2ZvcmVncm91bmRHUShbMCwwLDBdRidGLy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUYsNi1RMSZJbnZpc2libGVUaW1lcztGJ0YvRjJGNUY3RjlGO0Y9Rj8vRkJRJjAuMGVtRicvRkVGYW8tRiM2Jy1GTzYlUSVjb3NoRicvRlNGNEYvLUYsNi1RMCZBcHBseUZ1bmN0aW9uO0YnRi9GMkY1RjdGOUY7Rj1GP0Zgb0Ziby1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYjNihGKy1GTzYlUScmIzk1NTtGJ0Zob0YvLUYsNi1RIitGJ0YvRjJGNUY3RjlGO0Y9Rj9GQUZELUYjNidGY3BGXW8tRk82JVEieUYnRlJGVUZnbkYvRmduRi9GZ25GL0YvRmduRi9GZ25GLy1GIzYlLUYjNictRk82JVElc2luaEYnRmhvRi9GaW8tRl1wNiQtRiM2JUZjcEZnbkYvRi9GZ25GL0ZnbkYvLyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0Zeci8lKWJldmVsbGVkR0Y0RmduRi8=">LCQqKCZJIkNHNiI2IyIiIkYoLUklY29zaEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJjYjLCZJJ2xhbWJkYUdGJiEiIiomRjBGKEkieUdGJkYoRihGKC1JJXNpbmhHRis2I0YwRjFGMQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L20" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Y(y):=C[1]*cosh(lambda*(1-y))/sinh(lambda);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pi1JIllHNiI2I0kieUdGJSooJkkiQ0dGJTYjIiIiRiwtSSVjb3NoRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiMqJkknbGFtYmRhR0YlRiwsJkYsRixGJyEiIkYsRiwtSSVzaW5oR0YvNiNGNEY2">KigmSSJDRzYiNiMiIiJGJy1JJWNvc2hHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2IyomSSdsYW1iZGFHRiVGJywmRidGJ0kieUdGJSEiIkYnRictSSVzaW5oR0YqNiNGL0Yy</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L21" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Eq_X:=rhs(Eq)=lambda^2:</Text-field>
</Input>
</Group>
<Group labelreference="L22" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Eq_X:=expand(Eq_X*X(x));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkklRXFfWEc2Ii8sJi1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJYR0YkNiNJInhHRiQtSSIkR0YpNiRGLiIiIyEiIiomRi5GMy1GKDYkRitGLiIiIkYzKiZGK0Y3KUknbGFtYmRhR0YkRjJGNw==">LywmLUklZGlmZkclKnByb3RlY3RlZEc2JC1GJTYkLUkiWEc2IjYjSSJ4R0YsRi5GLiEiIiomRi5GL0YoIiIiRi8qJkYqRjFJJ2xhbWJkYUdGLCIiIw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L23" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">dsolve({Eq_X},X(x));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">PCMvLUkiWEc2IjYjSSJ4RzYiLCYqJkkkX0MxRzYiIiIiLUkoQmVzc2VsSkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYkIiIhKiZJJ2xhbWJkYUc2IiIiIkkieEc2IiIiIiIiIiIiIiomSSRfQzJHNiIiIiItSShCZXNzZWxZRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiQiIiEqJkknbGFtYmRhRzYiIiIiSSJ4RzYiIiIiIiIiIiIi</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L24" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">X(x):=c[1]*BesselJ(0,lambda*x)+c[2]*BesselY(0,lambda*x);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pi1JIlhHNiI2I0kieEdGJSwmKiYmSSJjR0YlNiMiIiJGLS1JKEJlc3NlbEpHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2JCIiISomSSdsYW1iZGFHRiVGLUYnRi1GLUYtKiYmRis2IyIiI0YtLUkoQmVzc2VsWUdGMEYzRi1GLQ==">LCYqJiZJImNHNiI2IyIiIkYoLUkoQmVzc2VsSkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJjYkIiIhKiZJJ2xhbWJkYUdGJkYoSSJ4R0YmRihGKEYoKiYmRiU2IyIiI0YoLUkoQmVzc2VsWUdGK0YuRihGKA==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L25" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Bc1:=diff(X(x),x)=0;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkQmMxRzYiLywmKigmSSJjR0YkNiMiIiJGKy1JKEJlc3NlbEpHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2JEYrKiZJJ2xhbWJkYUdGJEYrSSJ4R0YkRitGK0YzRishIiIqKCZGKTYjIiIjRistSShCZXNzZWxZR0YuRjFGK0YzRitGNSIiIQ==">LywmKigmSSJjRzYiNiMiIiJGKS1JKEJlc3NlbEpHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRic2JEYpKiZJJ2xhbWJkYUdGJ0YpSSJ4R0YnRilGKUYxRikhIiIqKCZGJjYjIiIjRiktSShCZXNzZWxZR0YsRi9GKUYxRilGMyIiIQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L26" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Bc2:=X(x)=0;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkQmMyRzYiLywmKiYmSSJjR0YkNiMiIiJGKy1JKEJlc3NlbEpHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2JCIiISomSSdsYW1iZGFHRiRGK0kieEdGJEYrRitGKyomJkYpNiMiIiNGKy1JKEJlc3NlbFlHRi5GMUYrRitGMg==">LywmKiYmSSJjRzYiNiMiIiJGKS1JKEJlc3NlbEpHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRic2JCIiISomSSdsYW1iZGFHRidGKUkieEdGJ0YpRilGKSomJkYmNiMiIiNGKS1JKEJlc3NlbFlHRixGL0YpRilGMA==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L27" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">BesselJ(0,0);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">IiIi</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L28" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">BesselY(0,0);</Text-field>
</Input>
<Output>
<Text-field style="Error" layout="Error">Error, (in BesselY) numeric exception: division by zero</Text-field>
</Output>
</Group>
<Group labelreference="L29" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">c[2]:=0;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJImNHNiI2IyIiIyIiIQ==">IiIh</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L30" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Eq_Bc2:=eval(subs(x=1,Bc2));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkknRXFfQmMyRzYiLyomJkkiY0dGJDYjIiIiRiotSShCZXNzZWxKRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiQiIiFJJ2xhbWJkYUdGJEYqRjE=">LyomJkkiY0c2IjYjIiIiRigtSShCZXNzZWxKRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YmNiQiIiFJJ2xhbWJkYUdGJkYoRi8=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L31" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Eq_Eig:=BesselJ(0,lambda)=0;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkknRXFfRWlnRzYiLy1JKEJlc3NlbEpHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2JCIiIUknbGFtYmRhR0YkRiw=">Ly1JKEJlc3NlbEpHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JCIiIUknbGFtYmRhR0YoRio=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L32" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">l[1]:=fsolve(Eq_Eig,lambda=0..3);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJImxHNiI2IyIiIiQiK2ViI1tTIyEiKg==">JCIrZWIjW1MjISIq</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L33" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">N:=20;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiTkc2IiIjPw==">IiM/</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L34" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from 2 to N do l[i]:=fsolve(Eq_Eig,lambda=l[i-1]..l[i-1]+4);od:</Text-field>
</Input>
</Group>
<Group labelreference="L35" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">seq(l[i],i=1..N);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NjYkIitlYiNbUyMhIiokIis1InkrXyZGJSQiKzh6c2AnKUYlJCIrV006ejYhIikkIityPDQkXCJGLCQiKyhSMXIhPUYsJCIrak87QEBGLCQiK2ByQ05DRiwkIis4ek1cRkYsJCIrWjFZaklGLCQiK0A/ZXhMRiwkIitOKTQ8cCRGLCQiK3dEJWUrJUYsJCIrciJ6Kj5WRiwkIitQKT1UaiVGLCQiKyEqNEVbXEYsJCIrJT0wQ0UmRiwkIit3NWJ3YkYsJCIrJFIpcCEqZUYsJCIrPnAlWz8nRiw=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L36" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">U:=eval(X(x)*Y(y)):</Text-field>
</Input>
</Group>
<Group labelreference="L37" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Un:=subs(c[1]=A[n]/C[1],lambda=lambda[n],U);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjVW5HNiIqKiZJIkFHRiQ2I0kibkdGJCIiIi1JKEJlc3NlbEpHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2JCIiISomJkknbGFtYmRhR0YkRihGKkkieEdGJEYqRiotSSVjb3NoR0YtNiMqJkYzRiosJkYqRipJInlHRiQhIiJGKkYqLUklc2luaEdGLTYjRjNGPA==">KiomSSJBRzYiNiNJIm5HRiUiIiItSShCZXNzZWxKRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiQiIiEqJiZJJ2xhbWJkYUdGJUYmRihJInhHRiVGKEYoLUklY29zaEdGKzYjKiZGMUYoLCZGKEYoSSJ5R0YlISIiRihGKC1JJXNpbmhHRis2I0YxRjo=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L38" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">u(x,y):=Sum(Un,n=1..N):</Text-field>
</Input>
</Group>
<Group labelreference="L39" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq_An:=eval(subs(y=0,u(x,y)))=rhs(bc3);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkmZXFfQW5HNiIvLUkkU3VtRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiQqKiZJIkFHRiQ2I0kibkdGJCIiIi1JKEJlc3NlbEpHRig2JCIiISomJkknbGFtYmRhR0YkRi9GMUkieEdGJEYxRjEtSSVjb3NoR0YoNiNGN0YxLUklc2luaEdGKEY8ISIiL0YwO0YxIiM/RjE=">Ly1JJFN1bUc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYkKiomSSJBR0YoNiNJIm5HRigiIiItSShCZXNzZWxKR0YlNiQiIiEqJiZJJ2xhbWJkYUdGKEYtRi9JInhHRihGL0YvLUklY29zaEdGJTYjRjVGLy1JJXNpbmhHRiVGOiEiIi9GLjtGLyIjP0Yv</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L40" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">phi[n]:=BesselJ(0,lambda[n]*x);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJJHBoaUc2IjYjSSJuR0YlLUkoQmVzc2VsSkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYkIiIhKiYmSSdsYW1iZGFHRiVGJiIiIkkieEdGJUYy">LUkoQmVzc2VsSkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYkIiIhKiYmSSdsYW1iZGFHRic2I0kibkdGJyIiIkkieEdGJ0Yv</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L41" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">r(x):=x;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pi1JInJHNiI2I0kieEdGJUYn">SSJ4RzYi</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L42" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">I1:=int(phi[n]^2*r(x),x=0..1):</Text-field>
</Input>
</Group>
<Group labelreference="L43" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">I2:=int(1*phi[n]*r(x),x=0..1):</Text-field>
</Input>
</Group>
<Group labelreference="L44" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">A[n]:=I2/I1/cosh(lambda[n])*sinh(lambda[n]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJIkFHNiI2I0kibkdGJSwkKjAiIiMiIiImSSdsYW1iZGFHRiVGJkYrLUkoQmVzc2VsSkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYkRitGLEYrKUkjUGlHRjEjRitGKkYrLCYqKEY0RispRixGKkYrKS1GLzYkIiIhRixGKkYrRisqKEY0RitGOUYrKUYuRipGK0YrISIiLUklY29zaEdGMDYjRixGQC1JJXNpbmhHRjBGQ0YrRis=">LCQqLiZJJ2xhbWJkYUc2IjYjSSJuR0YmIiIiLUkoQmVzc2VsSkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJjYkRilGJEYpSSNQaUdGLSNGKSIiIywmKihGMEYxRiRGMi1GKzYkIiIhRiRGMkYpKihGMEYxRiRGMkYqRjJGKSEiIi1JJWNvc2hHRiw2I0YkRjktSSVzaW5oR0YsRjxGKUYy</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L45" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">u(x,y):=eval(u(x,y));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pi1JInVHNiI2JEkieEdGJUkieUdGJS1JJFN1bUc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYkLCQqMiIiIyIiIiZJJ2xhbWJkYUdGJTYjSSJuR0YlRjItSShCZXNzZWxKR0YrNiRGMkYzRjIpSSNQaUdGLCNGMkYxRjIsJiooRjpGMilGM0YxRjIpLUY4NiQiIiFGM0YxRjJGMiooRjpGMkY/RjIpRjdGMUYyRjIhIiItSSVjb3NoR0YrNiNGM0ZGLUY4NiRGQyomRjNGMkYnRjJGMi1GSDYjKiZGM0YyLCZGMkYyRihGRkYyRjJGMi9GNjtGMiIjPw==">LUkkU3VtRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiQsJCowJkknbGFtYmRhR0YnNiNJIm5HRiciIiItSShCZXNzZWxKR0YkNiRGL0YrRi9JI1BpR0YlI0YvIiIjLCYqKEYzRjRGK0Y1LUYxNiQiIiFGK0Y1Ri8qKEYzRjRGK0Y1RjBGNUYvISIiLUklY29zaEdGJDYjRitGPC1GMTYkRjoqJkYrRi9JInhHRidGL0YvLUY+NiMqJkYrRi8sJkYvRi9JInlHRidGPEYvRi9GNS9GLjtGLyIjPw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L46" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i to N do lambda[i]:=l[i];od:</Text-field>
</Input>
</Group>
<Group labelreference="L47" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">ua:=evalf(u(x,y)):</Text-field>
</Input>
</Group>
<Group labelreference="L48" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">uu:=piecewise(y=0,1,y&gt;0,ua):</Text-field>
</Input>
</Group>
<Group labelreference="L49" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot3d(evalf(uu),x=0..1,y=1..0,axes=boxed,title=&quot;Figure Exp. 7.28.&quot;,labels=[x,y,&quot;u&quot;],orientation=[30,60]);</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="L50" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot([subs(y=0,uu),subs(y=0.1,uu),subs(y=0.2,uu),subs(y=0.3,uu),subs(y=0.4,uu),subs(y=1,uu)],x=0..1,axes=boxed,title=&quot;Figure Exp. 7.29.&quot;,thickness=5,labels=[x,&quot;u&quot;],legend=[&quot;y=0&quot;,&quot;y=0.1&quot;,&quot;y=0.2&quot;,&quot;y=0.3&quot;,&quot;y=0.4&quot;,&quot;y=1.0&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="true">[encoded data, 16044 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L53" 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>
</Worksheet>