<?xml version="1.0" encoding="UTF-8"?>
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    <Task-category name="&lt;default&gt;">
    </Task-category>
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<Annotation-table>
    <Annotation-category name="&lt;default&gt;">
    </Annotation-category>
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<Task>
</Task>
<Group labelreference="L49" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Example 7.6 Heat Conduction in a Slab with Radiation Boundary Conditions</Text-field>
</Input>
</Group>
<Group labelreference="L48" 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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">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2KVEocmVzdGFydEYnLyUnZmFtaWx5R1ErTW9ub3NwYWNlZEYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJTBmb250X3N0eWxlX25hbWVHUSxNYXBsZX5JbnB1dEYnLyUsbWF0aHZhcmlhbnRHUSVib2xkRicvJStmb250d2VpZ2h0R0Y9LUkjbW9HRiQ2MVEiOkYnRi9GMkY4RjtGPi8lJmZlbmNlR0Y3LyUqc2VwYXJhdG9yR0Y3LyUpc3RyZXRjaHlHRjcvJSpzeW1tZXRyaWNHRjcvJShsYXJnZW9wR0Y3LyUubW92YWJsZWxpbWl0c0dGNy8lJ2FjY2VudEdGNy8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlQ=</Equation></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="L50" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The governing equation, initial and boundary conditions are entered here:</Text-field>
</Input>
</Group>
<Group labelreference="L4" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq:=diff(u(x,t),t)=diff(u(x,t),x$2);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjZXFHNiIvLUklZGlmZkclKnByb3RlY3RlZEc2JC1JInVHRiQ2JEkieEdGJEkidEdGJEYuLUYnNiRGKi1JIiRHRig2JEYtIiIj">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJ1RzYiNiRJInhHRilJInRHRilGLC1GJDYkLUYkNiRGJ0YrRis=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L5" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">IC:=u(x,0)=1;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjSUNHNiIvLUkidUdGJDYkSSJ4R0YkIiIhIiIi">Ly1JInVHNiI2JEkieEdGJSIiISIiIg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L6" 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="PkkkYmMxRzYiLy1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJ1R0YkNiRJInhHRiRJInRHRiRGLSIiIQ==">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJ1RzYiNiRJInhHRilJInRHRilGKyIiIQ==</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)+u(x,t)=0;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkYmMyRzYiLywmLUklZGlmZkclKnByb3RlY3RlZEc2JC1JInVHRiQ2JEkieEdGJEkidEdGJEYuIiIiRitGMCIiIQ==">LywmLUklZGlmZkclKnByb3RlY3RlZEc2JC1JInVHNiI2JEkieEdGKkkidEdGKkYsIiIiRihGLiIiIQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L8" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Eq:=subs(u(x,t)=X(x)*T(t),eq):</Text-field>
</Input>
</Group>
<Group labelreference="L9" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Eq:=expand(Eq/X(x)/T(t)):</Text-field>
</Input>
</Group>
<Group labelreference="L10" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Eq_T:=lhs(Eq)=-lambda^2:</Text-field>
</Input>
</Group>
<Group labelreference="L11" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">T(t):=rhs(dsolve({Eq_T,T(0)=T0},T(t))):</Text-field>
</Input>
</Group>
<Group labelreference="L12" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Eq_X:=rhs(Eq)=-lambda^2:</Text-field>
</Input>
</Group>
<Group labelreference="L13" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Eq_X:=expand(Eq_X*X(x)):</Text-field>
</Input>
</Group>
<Group labelreference="L14" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">dsolve({Eq_X},X(x)):</Text-field>
</Input>
</Group>
<Group labelreference="L15" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">X(x):=c[1]*sin(lambda*x)+c[2]*cos(lambda*x):</Text-field>
</Input>
</Group>
<Group labelreference="L16" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Bc1:=diff(X(x),x)=0:</Text-field>
</Input>
</Group>
<Group labelreference="L17" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Bc2:=diff(X(x),x)+X(x)=0:</Text-field>
</Input>
</Group>
<Group labelreference="L18" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Eq_Bc1:=eval(subs(x=0,Bc1)):</Text-field>
</Input>
</Group>
<Group labelreference="L19" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">c[1]:=solve(Eq_Bc1,c[1]):</Text-field>
</Input>
</Group>
<Group labelreference="L20" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Eq_Bc2:=eval(subs(x=1,Bc2)):</Text-field>
</Input>
</Group>
<Group labelreference="L51" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The eigenvalue equation is:</Text-field>
</Input>
</Group>
<Group labelreference="L21" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Eq_Eig:=cos(lambda)-lambda*sin(lambda);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkknRXFfRWlnRzYiLCYtSSRjb3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0knbGFtYmRhR0YkIiIiKiZGLEYtLUkkc2luR0YoRitGLSEiIg==">LCYtSSRjb3NHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0knbGFtYmRhR0YoIiIiKiZGKkYrLUkkc2luR0YlRilGKyEiIg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L22" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">solve(Eq_Eig,lambda);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEnUm9vdE9mRicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RMCZBcHBseUZ1bmN0aW9uO0YnRjIvJSZmZW5jZUdGMS8lKnNlcGFyYXRvckdGMS8lKXN0cmV0Y2h5R0YxLyUqc3ltbWV0cmljR0YxLyUobGFyZ2VvcEdGMS8lLm1vdmFibGVsaW1pdHNHRjEvJSdhY2NlbnRHRjEvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZJLUkobWZlbmNlZEdGJDYkLUYjNiUtRiM2Jy1GIzYnLUYsNiVRI19aRicvRjBRJXRydWVGJy9GM1EnaXRhbGljRictRjY2LVExJkludmlzaWJsZVRpbWVzO0YnRjJGOUY7Rj1GP0ZBRkNGRUZHRkotRiM2Jy1GLDYlUSR0YW5GJ0YvRjJGNS1GTTYkLUYjNiVGVS8lK2ZvcmVncm91bmRHUShbMCwwLDBdRidGMkYyRmJvRjJGYm9GMi1GNjYtUSgmbWludXM7RidGMkY5RjtGPUY/RkFGQ0ZFL0ZIUSwwLjIyMjIyMjJlbUYnL0ZLRmlvLUkjbW5HRiQ2JFEiMUYnRjJGYm9GMkZib0YyRjJGYm9GMg==">LUknUm9vdE9mRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMsJiomSSNfWkdGJCIiIi1JJHRhbkdGJDYjRitGLEYsISIiRiw=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L52" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Maple predicts negative eigenvalues:</Text-field>
</Input>
</Group>
<Group labelreference="L23" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">fsolve(Eq_Eig,lambda);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">JCErISplTC4nKSEjNQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L53" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Positive eigenvalues can be obtained by specifying a positive range in the 'fsolve' command.</Text-field>
</Input>
</Group>
<Group labelreference="L24" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">fsolve(Eq_Eig,lambda=0..3);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">JCIrISplTC4nKSEjNQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L54" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The eigenvalue equation can be plotted as a function of the eigenvalue as:</Text-field>
</Input>
</Group>
<Group labelreference="L25" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot(Eq_Eig,lambda=0..20,thickness=3,title=&quot;Figure Exp. 7.14.&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="false">[encoded data, 6516 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L55" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The first 20 eigenvalues are obtained as:</Text-field>
</Input>
</Group>
<Group labelreference="L26" 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="L27" 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="PiZJImxHNiI2IyIiIiQiKyEqZUwuJykhIzU=">JCIrISplTC4nKSEjNQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L28" 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="L29" 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">NjYkIishKmVMLicpISM1JCIrZiU9Y1UkISIqJCIreiIpSFBrRigkIiswV0xIJipGKCQiK0EoR1hFIiEiKSQiKyhbR3JkIkYvJCIrJyo0QyEqPUYvJCIrdCdcTz8jRi8kIitMWUM8REYvJCIrJkdrNCRHRi8kIitrOXhXSkYvJCIrQUNrZU1GLyQiKyRHaER4JEYvJCIrTHFeJzMlRi8kIisjeiwwUyVGLyQiK3UoNFhyJUYvJCIrTW1gR11GLyQiK1shekRNJkYvJCIrR1dqY2NGLyQiK0oycXFmRi8=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L30" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">U:=eval(X(x)*T(t)):</Text-field>
</Input>
</Group>
<Group labelreference="L31" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Un:=subs(c[2]=A[n]/T0,lambda=lambda[n],U):</Text-field>
</Input>
</Group>
<Group labelreference="L32" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">u(x,t):=Sum(Un,n=1..infinity);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pi1JInVHNiI2JEkieEdGJUkidEdGJS1JJFN1bUc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYkKigmSSJBR0YlNiNJIm5HRiUiIiItSSRjb3NHRis2IyomJkknbGFtYmRhR0YlRjJGNEYnRjRGNC1JJGV4cEdGKzYjLCQqJilGOSIiI0Y0RihGNCEiIkY0L0YzO0Y0SSlpbmZpbml0eUdGLA==">LUkkU3VtRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiQqKCZJIkFHRic2I0kibkdGJyIiIi1JJGNvc0dGJDYjKiYmSSdsYW1iZGFHRidGLEYuSSJ4R0YnRi5GLi1JJGV4cEdGJDYjLCQqJkYzIiIjSSJ0R0YnRi4hIiJGLi9GLTtGLkkpaW5maW5pdHlHRiU=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L33" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq_An:=eval(subs(t=0,u(x,t)))=rhs(IC);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkmZXFfQW5HNiIvLUkkU3VtRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiQqJiZJIkFHRiQ2I0kibkdGJCIiIi1JJGNvc0dGKDYjKiYmSSdsYW1iZGFHRiRGL0YxSSJ4R0YkRjFGMS9GMDtGMUkpaW5maW5pdHlHRilGMQ==">Ly1JJFN1bUc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYkKiYmSSJBR0YoNiNJIm5HRigiIiItSSRjb3NHRiU2IyomJkknbGFtYmRhR0YoRi1GL0kieEdGKEYvRi8vRi47Ri9JKWluZmluaXR5R0YmRi8=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L34" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">phi[n]:=cos(lambda[n]*x):</Text-field>
</Input>
</Group>
<Group labelreference="L35" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">r(x):=1:</Text-field>
</Input>
</Group>
<Group labelreference="L36" 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="L37" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">IC;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">Ly1JInVHNiI2JEkieEdGJSIiISIiIg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L38" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">I2:=int(rhs(IC)*phi[n]*r(x),x=0..1):</Text-field>
</Input>
</Group>
<Group labelreference="L39" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">A[n]:=I2/I1;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PiZJIkFHNiI2I0kibkdGJSwkKigiIiMiIiItSSRzaW5HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2IyZJJ2xhbWJkYUdGJUYmRissJiomLUkkY29zR0YuRjFGK0YsRitGK0YyRishIiJGKw==">LCQqJi1JJHNpbkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjJkknbGFtYmRhR0YpNiNJIm5HRikiIiIsJiomLUkkY29zR0YmRipGL0YkRi9GL0YrRi8hIiIiIiM=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L40" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">u(x,t):=eval(u(x,t));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pi1JInVHNiI2JEkieEdGJUkidEdGJS1JJFN1bUc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYkLCQqLCIiIyIiIi1JJHNpbkdGKzYjJkknbGFtYmRhR0YlNiNJIm5HRiVGMiwmKiYtSSRjb3NHRitGNUYyRjNGMkYyRjZGMiEiIi1GPTYjKiZGNkYyRidGMkYyLUkkZXhwR0YrNiMsJComKUY2RjFGMkYoRjJGPkYyRjIvRjk7RjJJKWluZmluaXR5R0Ys">LUkkU3VtRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiQsJCoqLUkkc2luR0YkNiMmSSdsYW1iZGFHRic2I0kibkdGJyIiIiwmKiYtSSRjb3NHRiRGLUYyRitGMkYyRi5GMiEiIi1GNjYjKiZGLkYySSJ4R0YnRjJGMi1JJGV4cEdGJDYjLCQqJkYuIiIjSSJ0R0YnRjJGN0YyRkEvRjE7RjJJKWluZmluaXR5R0Yl</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L41" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">u(x,t):=subs(infinity=N,u(x,t)):</Text-field>
</Input>
</Group>
<Group labelreference="L42" 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="L56" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The transient analytical solution is:</Text-field>
</Input>
</Group>
<Group labelreference="L43" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Digits:=5:u(x,t):=evalf(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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">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</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L44" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">uu:=piecewise(t=0,rhs(IC),t&gt;0,u(x,t)):</Text-field>
</Input>
</Group>
<Group labelreference="L57" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The plots are obtained as:</Text-field>
</Input>
</Group>
<Group labelreference="L45" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">plot3d(uu,x=1..0,t=0.5..0,axes=boxed,title=&quot;Figure Exp. 7.15.&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">plot([subs(t=0,uu),subs(t=0.05,uu),subs(t=0.1,uu),subs(t=0.2,uu),subs(t=0.5,uu)],x=0..1,axes=boxed,title=&quot;Figure Exp. 7.16.&quot;,thickness=5,labels=[x,&quot;u&quot;],legend=[&quot;t=0&quot;,&quot;t=0.05&quot;,&quot;t=0.1&quot;,&quot;t=0.2&quot;,&quot;t=0.5&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, 15068 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L47" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
</Worksheet>