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<Text-field style="Text" layout="Normal">Example 8.6 Mass Transfer in a Spherical Pellet</Text-field>
<Text-field style="Text" layout="Normal">Example (8.1.6) is solved in Maple and the results obtained are given below:</Text-field>
</Input>
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<Group labelreference="L37" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="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">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</Equation></Text-field>
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<Group labelreference="L3" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal256">eq:=diff(u(x,t),t)=diff(u(x,t),x$2)+2/x*diff(u(x,t),x);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJ1RzYiNiRJInhHRilJInRHRilGLCwmLUYkNiQtRiQ2JEYnRitGKyIiIiooIiIjRjJGKyEiIkYwRjJGMg==</Equation></Text-field>
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<Group labelreference="L4" 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>
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<Group labelreference="L5" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc1:=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="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEkYmMxRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEjOj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GIzYnLUYjNictSSZtZnJhY0dGJDYoLUYjNiUtRjY2LVErJlBhcnRpYWxEO0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EmMC4wZW1GJy9GTkZmbi8lK2ZvcmVncm91bmRHUShbMCwwLDBdRidGOS1GIzYlLUYjNiZGWC1GLDYlUSJ4RidGL0YyRmhuRjlGaG5GOS8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGZ28vJSliZXZlbGxlZEdGPS1GNjYtUTEmSW52aXNpYmxlVGltZXM7RidGOUY7Rj5GQEZCRkRGRkZIRmVuRmduLUYjNictRiw2JVEidUYnRi9GMi1GNjYtUTAmQXBwbHlGdW5jdGlvbjtGJ0Y5RjtGPkZARkJGREZGRkhGZW5GZ24tSShtZmVuY2VkR0YkNiQtRiM2J0Zfby1GNjYtUSIsRidGOUY7L0Y/RjFGQEZCRkRGRkZIRmVuL0ZOUSwwLjMzMzMzMzNlbUYnLUYsNiVRInRGJ0YvRjJGaG5GOUY5RmhuRjlGaG5GOS1GNjYtUSI9RidGOUY7Rj5GQEZCRkRGRkZIRkpGTS1JI21uR0YkNiRRIjBGJ0Y5RmhuRjlGaG5GOQ==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJ1RzYiNiRJInhHRilJInRHRilGKyIiIQ==</Equation></Text-field>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc2:=u(x,t)=1;</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly1JInVHNiI2JEkieEdGJUkidEdGJSIiIg==</Equation></Text-field>
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<Group labelreference="L7" 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="L8" 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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">LyomSSJzRzYiIiIiLUkiVUdGJTYjSSJ4R0YlRiYsJi1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtRi02JEYnRipGKkYmKigiIiNGJkYqISIiRjBGJkYm</Equation></Text-field>
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<Group labelreference="L9" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal256">bc1:=laplace(bc1,t,s):</Text-field>
</Input>
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<Group labelreference="L10" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc1:=subs(diff(laplace(u(x,t),t,s),x)=D(U)(0),laplace(u(x,t),t,s)=U(0),bc1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly0tSSJERzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJIlVHRik2IyIiIUYt</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L11" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal256">bc2:=laplace(bc2,t,s):</Text-field>
</Input>
</Group>
<Group labelreference="L12" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">bc2:=subs(diff(laplace(u(x,t),t,s),x)=D(U)(1),laplace(u(x,t),t,s)=U(1),bc2);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly1JIlVHNiI2IyIiIiokSSJzR0YlISIi</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L13" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">U(x):=rhs(dsolve({eqs,bc2},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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">LCYqKEkkX0MxRzYiIiIiSSJ4R0YlISIiLUklc2luaEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjKiYpSSJzR0YlI0YmIiIjRiZGJ0YmRiZGJiosLCgqKEYxRiZGJEYmLUkkZXhwR0YrNiMsJComIiIpRiZGMEYmRiZGJkYmKihGMUYmRiRGJi1GODYjLCQqJiIiJ0YmRjBGJkYmRiZGKComRjNGJi1GODYjLCQqJiIiKEYmRjBGJkYmRiZGKEYmRjFGKCwmRjdGJkY+RiZGKEYnRigtSSVjb3NoR0YrRi5GJkYo</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L14" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">U(x):=subs(_C2=0,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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">LCYqKEkkX0MxRzYiIiIiSSJ4R0YlISIiLUklc2luaEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjKiYpSSJzR0YlI0YmIiIjRiZGJ0YmRiZGJiosLCgqKEYxRiZGJEYmLUkkZXhwR0YrNiMsJComIiIpRiZGMEYmRiZGJkYmKihGMUYmRiRGJi1GODYjLCQqJiIiJ0YmRjBGJkYmRiZGKComRjNGJi1GODYjLCQqJiIiKEYmRjBGJkYmRiZGKEYmRjFGKCwmRjdGJkY+RiZGKEYnRigtSSVjb3NoR0YrRi5GJkYo</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L15" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">convert(U(x),exp);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCYqKEkkX0MxRzYiIiIiSSJ4R0YlISIiLCYqJiNGJiIiI0YmLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiMqJilJInNHRiVGK0YmRidGJkYmRiYqJkYrRiYtRi42IywkRjNGKEYmRihGJkYmKiwsKCooRjVGJkYkRiYtRi42IywkKiYiIilGJkY0RiZGJkYmRiYqKEY1RiZGJEYmLUYuNiMsJComIiInRiZGNEYmRiZGJkYoKiZGLEYmLUYuNiMsJComIiIoRiZGNEYmRiZGJkYoRiZGNUYoLCZGPUYmRkNGJkYoRidGKCwmRipGJkY2RiZGJkYo</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L16" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">U1s:=exp(s^(1/2))/s/(exp(s^(1/2))^2-1)*exp(s^(1/2)*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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">KiwtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IyokKUkic0dGKCMiIiIiIiNGLkYuRiwhIiIsJiokKUYjRi9GLkYuRi5GMEYwLUYkNiMqJkYrRi5JInhHRihGLkYuRjdGMA==</Equation></Text-field>
</Output>
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<Group labelreference="L17" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">U2s:=-exp(s^(1/2))/s/(exp(s^(1/2))^2-1)*exp(-s^(1/2)*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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">LCQqLC1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjKiQpSSJzR0YpIyIiIiIiI0YvRi9GLSEiIiwmKiQpRiRGMEYvRi9GL0YxRjEtRiU2IywkKiZGLEYvSSJ4R0YpRi9GMUYvRjlGMUYx</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L18" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">U1S:=series(subs(exp(s^(1/2))=1/S,U1s),S):</Text-field>
</Input>
</Group>
<Group labelreference="L19" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">U1S:=subs(S=exp(-s^(1/2)),U1S):</Text-field>
</Input>
</Group>
<Group labelreference="L20" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">simplify(U1S);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KigsKi1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjKiYpSSJzR0YpIyIiIiIiI0YvLCZJInhHRilGL0YvISIiRi9GLy1GJTYjKiZGLEYvLCZGMkYvIiIkRjNGL0YvLUYlNiMqJkYsRi8sJkYyRi8iIiZGM0YvRi8qKC1JIk9HRic2Iy1GJTYjLCQqJiIiKEYvRixGL0YzRi9GLUYvRjJGL0YvRi9GLUYzRjJGMw==</Equation></Text-field>
</Output>
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<Group labelreference="L21" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">U1S:=1/x*Sum(exp(s^(1/2)*(x-2*n+1))/s,n=1..infinity);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KiZJInhHNiIhIiItSSRTdW1HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2JComLUkkZXhwR0YoNiMqJilJInNHRiQjIiIiIiIjRjQsKEYjRjQqJkY1RjRJIm5HRiRGNEYlRjRGNEY0RjRGMkYlL0Y4O0Y0SSlpbmZpbml0eUdGKUY0</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L22" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">u1s:=exp(s^(1/2)*(x-2*n+1))/s;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KiYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2IyomKUkic0dGKCMiIiIiIiNGLiwoSSJ4R0YoRi4qJkYvRi5JIm5HRihGLiEiIkYuRi5GLkYuRixGNA==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L23" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">u1t:=invlaplace(u1s,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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">LUkraW52bGFwbGFjZUc2IjYlKiYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2IyomKUkic0dGJCMiIiIiIiNGMSwoSSJ4R0YkRjEqJkYyRjFJIm5HRiRGMSEiIkYxRjFGMUYxRi9GN0YvSSJ0R0Yk</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L24" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">U1t:=1/x*Sum(u1t,n=1..infinity);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KiZJInhHNiIhIiItSSRTdW1HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2JC1JK2ludmxhcGxhY2VHRiQ2JSomLUkkZXhwR0YoNiMqJilJInNHRiQjIiIiIiIjRjcsKEYjRjcqJkY4RjdJIm5HRiRGN0YlRjdGN0Y3RjdGNUYlRjVJInRHRiQvRjs7RjdJKWluZmluaXR5R0YpRjc=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L25" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">U2S:=series(subs(exp(s^(1/2))=1/S,U2s),S):</Text-field>
</Input>
</Group>
<Group labelreference="L26" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">U2S:=subs(S=exp(-s^(1/2)),U2S):</Text-field>
</Input>
</Group>
<Group labelreference="L27" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">simplify(U2S);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCQqKCwqLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMsJComKUkic0dGKiMiIiIiIiNGMSwmSSJ4R0YqRjFGMUYxRjEhIiJGMS1GJjYjLCQqJkYuRjEsJkY0RjEiIiRGMUYxRjVGMS1GJjYjLCQqJkYuRjEsJkY0RjEiIiZGMUYxRjVGMSooLUkiT0dGKDYjLUYmNiMsJComIiIoRjFGLkYxRjVGMUYvRjFGNEYxRjVGMUYvRjVGNEY1RjU=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L28" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">U2S:=-1/x*Sum(exp(-s^(1/2)*(x+2*n-1))/s,n=1..infinity);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEkVTJTRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEjOj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GIzYmLUY2Ni1RKiZ1bWludXMwO0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EsMC4yMjIyMjIyZW1GJy9GTkZVLUkmbWZyYWNHRiQ2KC1GIzYlLUYjNictSSttdW5kZXJvdmVyR0YkNictRjY2L1EmJlN1bTtGJy8lK2ZvcmVncm91bmRHUS5bMTQ0LDE0NCwxNDRdRidGOS9JK21zZW1hbnRpY3NHRiRRJmluZXJ0RidGO0Y+L0ZBRjFGQi9GRUYxL0ZHRjFGSC9GS1EmMC4wZW1GJy9GTlEsMC4xNjY2NjY3ZW1GJy1GIzYnLUYsNiVRIm5GJ0YvRjItRjY2LVEiPUYnRjlGO0Y+RkBGQkZERkZGSEZKRk0tSSNtbkdGJDYkUSIxRidGOS9GX29RKFswLDAsMF1GJ0Y5LUYsNiVRKCYjODczNDtGJ0YvRjIvJSdhY2NlbnRHRj0vJSxhY2NlbnR1bmRlckdGPS1JJ21zcGFjZUdGJDYmLyUnaGVpZ2h0R1EmMC4wZXhGJy8lJndpZHRoR1EkNS4wRicvJSZkZXB0aEdGZXEvJSpsaW5lYnJlYWtHUSVhdXRvRictRlg2KC1GIzYlLUklbXN1cEdGJDYlLUY2Ni1RLyZFeHBvbmVudGlhbEU7RidGOUY7Rj5GQEZCRkRGRkZIRmdvL0ZOUSwwLjExMTExMTFlbUYnLUYjNiZGUS1GIzYmLUkmbXNxcnRHRiQ2Iy1GLDYlUSJzRidGL0YyLUY2Ni1RMSZJbnZpc2libGVUaW1lcztGJ0Y5RjtGPkZARkJGREZGRkhGZ28vRk5GaG8tSShtZmVuY2VkR0YkNiQtRiM2KC1GLDYlUSJ4RidGL0YyLUY2Ni1RIitGJ0Y5RjtGPkZARkJGREZGRkhGVEZWLUYjNiYtRmRwNiRRIjJGJ0Y5RmRzRl1wRjktRjY2LVEoJm1pbnVzO0YnRjlGO0Y+RkBGQkZERkZGSEZURlZGY3BGOUY5RjlGZ3BGOS8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGZ3BGOS1GIzYlRmFzRmdwRjkvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRmV1LyUpYmV2ZWxsZWRHRj1GZ3BGOUZncEY5LUYjNiVGXXRGZ3BGOUZgdUZjdUZmdUZodUZncEY5RmdwRjk=">LCQqJkkieEc2IiEiIi1JJFN1bUc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYkKiYtSSRleHBHRik2IywkKiYpSSJzR0YlIyIiIiIiI0Y2LChGJEY2KiZGN0Y2SSJuR0YlRjZGNkY2RiZGNkYmRjZGNEYmL0Y6O0Y2SSlpbmZpbml0eUdGKkY2RiY=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L29" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">u2s:=exp(-s^(1/2)*(x+2*n-1))/s:</Text-field>
</Input>
</Group>
<Group labelreference="L30" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">u2t:=invlaplace(u2s,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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">LUkraW52bGFwbGFjZUc2IjYlKiYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2IyomLChJInhHRiQhIiIqJiIiIyIiIkkibkdGJEYzRjBGM0YzRjMpSSJzR0YkI0YzRjJGM0YzRjZGMEY2SSJ0R0Yk</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L31" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">U2t:=-1/x*Sum(u2t,n=1..infinity);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEkVTJ0RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEjOj1GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GIzYmLUY2Ni1RKiZ1bWludXMwO0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EsMC4yMjIyMjIyZW1GJy9GTkZVLUkmbWZyYWNHRiQ2KC1GIzYlLUYjNictSSttdW5kZXJvdmVyR0YkNictRjY2L1EmJlN1bTtGJy8lK2ZvcmVncm91bmRHUS5bMTQ0LDE0NCwxNDRdRidGOS9JK21zZW1hbnRpY3NHRiRRJmluZXJ0RidGO0Y+L0ZBRjFGQi9GRUYxL0ZHRjFGSC9GS1EmMC4wZW1GJy9GTlEsMC4xNjY2NjY3ZW1GJy1GIzYnLUYsNiVRIm5GJ0YvRjItRjY2LVEiPUYnRjlGO0Y+RkBGQkZERkZGSEZKRk0tSSNtbkdGJDYkUSIxRidGOS9GX29RKFswLDAsMF1GJ0Y5LUYsNiVRKCYjODczNDtGJ0YvRjIvJSdhY2NlbnRHRj0vJSxhY2NlbnR1bmRlckdGPS1JJ21zcGFjZUdGJDYmLyUnaGVpZ2h0R1EmMC4wZXhGJy8lJndpZHRoR1EkNS4wRicvJSZkZXB0aEdGZXEvJSpsaW5lYnJlYWtHUSVhdXRvRictRiM2Jy1GLDYlUStpbnZsYXBsYWNlRidGL0YyLUY2Ni1RMCZBcHBseUZ1bmN0aW9uO0YnRjlGO0Y+RkBGQkZERkZGSEZnby9GTkZoby1JKG1mZW5jZWRHRiQ2JC1GIzYpLUZYNigtRiM2JS1JJW1zdXBHRiQ2JS1GNjYtUS8mRXhwb25lbnRpYWxFO0YnRjlGO0Y+RkBGQkZERkZGSEZnby9GTlEsMC4xMTExMTExZW1GJy1GIzYmLUZocjYkLUYjNilGUS1GLDYlUSJ4RidGL0YyLUY2Ni1RKCZtaW51cztGJ0Y5RjtGPkZARkJGREZGRkhGVEZWLUYjNiYtRmRwNiRRIjJGJ0Y5LUY2Ni1RMSZJbnZpc2libGVUaW1lcztGJ0Y5RjtGPkZARkJGREZGRkhGZ29GZnJGXXBGOS1GNjYtUSIrRidGOUY7Rj5GQEZCRkRGRkZIRlRGVkZjcEY5RjlGaXQtSSZtc3FydEdGJDYjLUYsNiVRInNGJ0YvRjJGOS8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGZ3BGOS1GIzYlRmJ1RmdwRjkvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRl92LyUpYmV2ZWxsZWRHRj0tRjY2LVEiLEYnRjlGOy9GP0YxRkBGQkZERkZGSEZnby9GTlEsMC4zMzMzMzMzZW1GJ0ZidUZkdi1GLDYlUSJ0RidGL0YyRmdwRjlGOUZncEY5RmdwRjlGZ3BGOS1GIzYlRl50RmdwRjlGanVGXXZGYHZGYnZGZ3BGOUZncEY5">LCQqJkkieEc2IiEiIi1JJFN1bUc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYkLUkraW52bGFwbGFjZUdGJTYlKiYtSSRleHBHRik2IyomLChGJEYmKiYiIiMiIiJJIm5HRiVGOEYmRjhGOEY4KUkic0dGJSNGOEY3RjhGOEY7RiZGO0kidEdGJS9GOTtGOEkpaW5maW5pdHlHRipGOEYm</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L32" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Ut:=U1t+U2t;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCYqJkkieEc2IiEiIi1JJFN1bUc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYkLUkraW52bGFwbGFjZUdGJTYlKiYtSSRleHBHRik2IyomKUkic0dGJSMiIiIiIiNGOCwoRiRGOComRjlGOEkibkdGJUY4RiZGOEY4RjhGOEY2RiZGNkkidEdGJS9GPDtGOEkpaW5maW5pdHlHRipGOEY4KiZGJEYmLUYoNiQtRi42JSomLUYyNiMqJiwoRiRGJkY7RiZGOEY4RjhGNUY4RjhGNkYmRjZGPUY+RjhGJg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L33" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">u:=subs(infinity=N,Ut):</Text-field>
</Input>
</Group>
<Group labelreference="L34" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">u:=subs(N=20,u);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEidUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIzo9RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtRiM2Ji1JJm1mcmFjR0YkNigtRiM2JS1GIzYnLUkrbXVuZGVyb3ZlckdGJDYnLUY2Ni9RJiZTdW07RicvJStmb3JlZ3JvdW5kR1EuWzE0NCwxNDQsMTQ0XUYnRjkvSSttc2VtYW50aWNzR0YkUSZpbmVydEYnRjtGPi9GQUYxRkIvRkVGMS9GR0YxRkgvRktRJjAuMGVtRicvRk5RLDAuMTY2NjY2N2VtRictRiM2Jy1GLDYlUSJuRidGL0YyLUY2Ni1RIj1GJ0Y5RjtGPkZARkJGREZGRkhGSkZNLUkjbW5HRiQ2JFEiMUYnRjkvRmluUShbMCwwLDBdRidGOS1GXnA2JFEjMjBGJ0Y5LyUnYWNjZW50R0Y9LyUsYWNjZW50dW5kZXJHRj0tSSdtc3BhY2VHRiQ2Ji8lJ2hlaWdodEdRJjAuMGV4RicvJSZ3aWR0aEdRJDUuMEYnLyUmZGVwdGhHRl9xLyUqbGluZWJyZWFrR1ElYXV0b0YnLUYjNictRiw2JVEraW52bGFwbGFjZUYnRi9GMi1GNjYtUTAmQXBwbHlGdW5jdGlvbjtGJ0Y5RjtGPkZARkJGREZGRkhGYW8vRk5GYm8tSShtZmVuY2VkR0YkNiQtRiM2KS1GUjYoLUYjNiUtSSVtc3VwR0YkNiUtRjY2LVEvJkV4cG9uZW50aWFsRTtGJ0Y5RjtGPkZARkJGREZGRkhGYW8vRk5RLDAuMTExMTExMWVtRictRiM2Ji1JJm1zcXJ0R0YkNiMtRiw2JVEic0YnRi9GMi1GNjYtUTEmSW52aXNpYmxlVGltZXM7RidGOUY7Rj5GQEZCRkRGRkZIRmFvRmByLUZicjYkLUYjNigtRiw2JVEieEYnRi9GMi1GNjYtUSgmbWludXM7RidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSwwLjIyMjIyMjJlbUYnL0ZORmh0LUYjNiYtRl5wNiRRIjJGJ0Y5RmpzRmdvRjktRjY2LVEiK0YnRjlGO0Y+RkBGQkZERkZGSEZndEZpdEZdcEY5RjlGOS8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGYXBGOS1GIzYlRmdzRmFwRjkvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRlx2LyUpYmV2ZWxsZWRHRj0tRjY2LVEiLEYnRjlGOy9GP0YxRkBGQkZERkZGSEZhby9GTlEsMC4zMzMzMzMzZW1GJ0Znc0Zhdi1GLDYlUSJ0RidGL0YyRmFwRjlGOUZhcEY5RmFwRjlGYXBGOS1GIzYlRmF0RmFwRjlGZ3VGanVGXXZGX3ZGZHQtRlI2KC1GIzYlLUYjNidGWEZqcC1GIzYnRmpxRl1yLUZicjYkLUYjNiktRlI2KC1GIzYlLUZbczYlRl1zLUYjNiYtRmJyNiQtRiM2KS1GNjYtUSomdW1pbnVzMDtGJ0Y5RjtGPkZARkJGREZGRkhGZ3RGaXRGYXRGZHRGanRGX3VGXXBGOUY5RmpzRmRzRjlGYnVGYXBGOUZldUZndUZqdUZddkZfdkZhdkZnc0ZhdkZndkZhcEY5RjlGYXBGOUZhcEY5RmFwRjlGanZGZ3VGanVGXXZGX3ZGOUZhcEY5">LCYqJkkieEc2IiEiIi1JJFN1bUc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYkLUkraW52bGFwbGFjZUdGJTYlKiYtSSRleHBHRik2IyomKUkic0dGJSMiIiIiIiNGOCwoRiRGOComRjlGOEkibkdGJUY4RiZGOEY4RjhGOEY2RiZGNkkidEdGJS9GPDtGOCIjP0Y4RjgqJkYkRiYtRig2JC1GLjYlKiYtRjI2IyomLChGJEYmRjtGJkY4RjhGOEY1RjhGOEY2RiZGNkY9Rj5GOEYm</Equation></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot3d(u,x=1e-6..1,t=1e-6..0.1,axes=boxed,title=&quot;Figure Exp. 8.11.&quot;,labels=[x,t,&quot;u&quot;],orientation=[-150,60]);</Text-field>
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<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>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot([subs(t=1e-6,u),subs(t=1e-2,u),subs(t=0.05,u),subs(t=0.1,u)],x=0..1,axes=boxed,title=&quot;Figure Exp. 8.12.&quot;,thickness=5,labels=[x,&quot;u&quot;]);</Text-field>
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<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">[encoded data, 9436 characters]</Plot></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EhRicvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JSFH</Equation></Text-field>
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