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<Input>
<Text-field style="Heading 3" italic="false" layout="Heading 3"><Font italic="false">Example 3.2.15  Graetz Problem-Shooting Technique</Font></Text-field>
</Input>
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<Group labelreference="L41" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">restart:</Text-field>
</Input>
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<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(y(x),x$2)+1/x*diff(y(x),x)+lambda^2*(1-x^2)*y(x);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjZXFHNiIsKC1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJ5R0YkNiNJInhHRiQtSSIkR0YoNiRGLSIiIyIiIiomRi0hIiItRic2JEYqRi1GMkYyKigpSSdsYW1iZGFHRiRGMUYyLCZGMkYyKiQpRi1GMUYyRjRGMkYqRjJGMg==">LCgtSSVkaWZmRyUqcHJvdGVjdGVkRzYkLUYkNiQtSSJ5RzYiNiNJInhHRitGLUYtIiIiKiZGLSEiIkYnRi5GLiooKUknbGFtYmRhR0YrIiIjRi4sJkYuRi4qJClGLUY0Ri5GMEYuRilGLkYu</Equation></Text-field>
</Output>
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<Group labelreference="L5" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eqlambda:=subs(y(x)=Y(x,lambda),eq);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkpZXFsYW1iZGFHNiIsKC1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJZR0YkNiRJInhHRiRJJ2xhbWJkYUdGJC1JIiRHRig2JEYtIiIjIiIiKiZGLSEiIi1GJzYkRipGLUYzRjMqKClGLkYyRjMsJkYzRjMqJClGLUYyRjNGNUYzRipGM0Yz">LCgtSSVkaWZmRyUqcHJvdGVjdGVkRzYkLUYkNiQtSSJZRzYiNiRJInhHRitJJ2xhbWJkYUdGK0YtRi0iIiIqJkYtISIiRidGL0YvKigpRi4iIiNGLywmRi9GLyokKUYtRjRGL0YxRi9GKUYvRi8=</Equation></Text-field>
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<Group labelreference="L6" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eqlambda:=diff(eqlambda,lambda);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkpZXFsYW1iZGFHNiIsKi1JJWRpZmZHJSpwcm90ZWN0ZWRHNiUtSSJZR0YkNiRJInhHRiRJJ2xhbWJkYUdGJEYuLUkiJEdGKDYkRi0iIiMiIiIqJkYtISIiLUYnNiVGKkYuRi1GM0YzKipGMkYzRi5GMywmRjNGMyokKUYtRjJGM0Y1RjNGKkYzRjMqKClGLkYyRjNGOUYzLUYnNiRGKkYuRjNGMw==">LCotSSVkaWZmRyUqcHJvdGVjdGVkRzYkLUYkNiQtRiQ2JC1JIllHNiI2JEkieEdGLUknbGFtYmRhR0YtRjBGL0YvIiIiKiZGLyEiIkYnRjFGMSoqIiIjRjFGMEYxLCZGMUYxKiQpRi9GNUYxRjNGMUYrRjFGMSooKUYwRjVGMUY2RjFGKUYxRjE=</Equation></Text-field>
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<Group labelreference="L7" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eqlambda:=subs(diff(Y(x,lambda),lambda)=y2(x),eqlambda);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkpZXFsYW1iZGFHNiIsKi1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSN5MkdGJDYjSSJ4R0YkLUkiJEdGKDYkRi0iIiMiIiIqJkYtISIiLUYnNiRGKkYtRjJGMioqRjFGMkknbGFtYmRhR0YkRjIsJkYyRjIqJClGLUYxRjJGNEYyLUkiWUdGJDYkRi1GOEYyRjIqKClGOEYxRjJGOUYyRipGMkYy">LCotSSVkaWZmRyUqcHJvdGVjdGVkRzYkLUYkNiQtSSN5Mkc2IjYjSSJ4R0YrRi1GLSIiIiomRi0hIiJGJ0YuRi4qKiIiI0YuSSdsYW1iZGFHRitGLiwmRi5GLiokKUYtRjJGLkYwRi4tSSJZR0YrNiRGLUYzRi5GLiooKUYzRjJGLkY0Ri5GKUYuRi4=</Equation></Text-field>
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<Group labelreference="L8" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eqlambda:=subs(Y(x,lambda)=y(x),eqlambda);</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkpZXFsYW1iZGFHNiIsKi1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSN5MkdGJDYjSSJ4R0YkLUkiJEdGKDYkRi0iIiMiIiIqJkYtISIiLUYnNiRGKkYtRjJGMioqRjFGMkknbGFtYmRhR0YkRjIsJkYyRjIqJClGLUYxRjJGNEYyLUkieUdGJEYsRjJGMiooKUY4RjFGMkY5RjJGKkYyRjI=">LCotSSVkaWZmRyUqcHJvdGVjdGVkRzYkLUYkNiQtSSN5Mkc2IjYjSSJ4R0YrRi1GLSIiIiomRi0hIiJGJ0YuRi4qKiIiI0YuSSdsYW1iZGFHRitGLiwmRi5GLiokKUYtRjJGLkYwRi4tSSJ5R0YrRixGLkYuKigpRjNGMkYuRjRGLkYpRi5GLg==</Equation></Text-field>
</Output>
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<Group labelreference="L9" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">vars:=(y(x),y2(x));</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkldmFyc0c2IjYkLUkieUdGJDYjSSJ4R0YkLUkjeTJHRiRGKA==">NiQtSSJ5RzYiNiNJInhHRiUtSSN5MkdGJUYm</Equation></Text-field>
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<Group labelreference="L10" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">lambda0:=1;</Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkobGFtYmRhMEc2IiIiIg==">IiIi</Equation></Text-field>
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<Group labelreference="L11" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eqs:=subs(lambda=lambda0,eq),subs(lambda=lambda0,eqlambda);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkZXFzRzYiNiQsKC1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJ5R0YkNiNJInhHRiQtSSIkR0YpNiRGLiIiIyIiIiomRi4hIiItRig2JEYrRi5GM0YzKiYsJkYzRjMqJClGLkYyRjNGNUYzRitGM0YzLCotRig2JC1JI3kyR0YkRi1GL0YzKiZGLkY1LUYoNiRGP0YuRjNGMyooRjJGM0Y5RjNGK0YzRjMqJkY5RjNGP0YzRjM=">NiQsKC1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtRiU2JC1JInlHNiI2I0kieEdGLEYuRi4iIiIqJkYuISIiRihGL0YvKiYsJkYvRi8qJClGLiIiI0YvRjFGL0YqRi9GLywqLUYlNiQtRiU2JC1JI3kyR0YsRi1GLkYuRi8qJkYuRjFGOkYvRi8qKEY2Ri9GM0YvRipGL0YvKiZGM0YvRjxGL0Yv</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L12" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">e:=1e-6;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiZUc2IiQiIiIhIic=">JCIiIiEiJw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L13" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">ICs:=(D(y)(0)=0,y(0)=1,y2(0)=0,D(y2)(0)=0);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkSUNzRzYiNiYvLS1JIkRHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0kieUdGJDYjIiIhRjAvLUYuRi8iIiIvLUkjeTJHRiRGL0YwLy0tRik2I0Y2Ri9GMA==">NiYvLS1JIkRHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kieUdGKjYjIiIhRi4vLUYsRi0iIiIvLUkjeTJHRipGLUYuLy0tRiY2I0Y0Ri1GLg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L14" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">sol:=dsolve({eqs,ICs},{vars},type=numeric);</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>
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<Group labelreference="L15" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">sol(1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NycvSSJ4RzYiJCIiIiIiIS8tSSJ5R0YlNiNGJCQiMyQ+VV4nKWYkeS0jKSEjPS8tSSVkaWZmRyUqcHJvdGVjdGVkRzYkRipGJCQhM1s7JyozaGo6QUJGLy8tSSN5MkdGJUYsJCEzdidlLSpmISlvVE1GLy8tRjI2JEY4RiQkITNxJVJpJj0iNHVIJUYv</Equation></Text-field>
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<Group labelreference="L16" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">e:=1e-6;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkiZUc2IiQiIiIhIic=">JCIiIiEiJw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L17" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">ICs:=(D(y)(e)=0,y(e)=1,y2(e)=0,D(y2)(e)=0);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkSUNzRzYiNiYvLS1JIkRHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2I0kieUdGJDYjJCIiIiEiJyIiIS8tRi5GL0YxLy1JI3kyR0YkRi9GMy8tLUYpNiNGOEYvRjM=">NiYvLS1JIkRHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kieUdGKjYjJCIiIiEiJyIiIS8tRixGLUYvLy1JI3kyR0YqRi1GMS8tLUYmNiNGNkYtRjE=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L18" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">sol:=dsolve({eqs,ICs},{vars},type=numeric);</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="L19" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">sol(1);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NycvSSJ4RzYiJCIiIiIiIS8tSSJ5R0YlNiNGJCQiM3JHa0wkbyR5LSMpISM9Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiRGKkYkJCEzZGxYIT45ZEBLI0YvLy1JI3kyR0YlRiwkITM1LyJvNWsob1RNRi8vLUYyNiRGOEYkJCEzLXk4bzFBVChIJUYv</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L20" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">ypred:=rhs(sol(1)[2]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkmeXByZWRHNiIkIjNyR2tMJG8keS0jKSEjPQ==">JCIzckdrTCRvJHktIykhIz0=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L21" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">y2pred:=rhs(sol(1)[4]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkneTJwcmVkRzYiJCEzNS8ibzVrKG9UTSEjPQ==">JCEzNS8ibzVrKG9UTSEjPQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L22" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">lambda1:=lambda0+(0-ypred)/y2pred;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkobGFtYmRhMUc2IiQiK3ozTyRRJCEiKg==">JCIrejNPJFEkISIq</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L23" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">err:=lambda1-lambda0;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkZXJyRzYiJCIrejNPJFEjISIq">JCIrejNPJFEjISIq</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L24" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">lambda0:=lambda1;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkobGFtYmRhMEc2IiQiK3ozTyRRJCEiKg==">JCIrejNPJFEkISIq</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L25" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">k:=1;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pkkia0c2IiIiIg==">IiIi</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L26" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">while err&gt;1e-6 do</Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eqs:=subs(lambda=lambda0,eq),subs(lambda=lambda0,eqlambda);</Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">sol:=dsolve({eqs,ICs},{vars},type=numeric);</Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">ypred:=rhs(sol(1)[2]);</Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">y2pred:=rhs(sol(1)[4]);</Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">lambda1:=lambda0+(0-ypred)/y2pred;</Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">err:=abs(lambda1-lambda0);</Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">lambda0:=lambda1;k:=k+1;</Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">end;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkZXFzRzYiNiQsKC1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJ5R0YkNiNJInhHRiQtSSIkR0YpNiRGLiIiIyIiIiomRi4hIiItRig2JEYrRi5GM0YzKigkIislMzhaOSIhIilGMywmRjNGMyokKUYuRjJGM0Y1RjNGK0YzRjMsKi1GKDYkLUkjeTJHRiRGLUYvRjMqJkYuRjUtRig2JEZCRi5GM0YzKigkIitlPHNtbiEiKkYzRjxGM0YrRjNGMyooRjlGM0Y8RjNGQkYzRjM=">NiQsKC1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtRiU2JC1JInlHNiI2I0kieEdGLEYuRi4iIiIqJkYuISIiRihGL0YvKigkIislMzhaOSIhIilGLywmRi9GLyokKUYuIiIjRi9GMUYvRipGL0YvLCotRiU2JC1GJTYkLUkjeTJHRixGLUYuRi5GLyomRi5GMUY9Ri9GLyooJCIrZTxzbW4hIipGL0Y2Ri9GKkYvRi8qKEYzRi9GNkYvRj9GL0Yv</Equation></Text-field>
</Output>
<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>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkmeXByZWRHNiIkITM+QiYqcGQ/ejdJISM9">JCEzPkImKnBkP3o3SSEjPQ==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkneTJwcmVkRzYiJCEzS2lVIlImKXkoNFAhIz0=">JCEzS2lVIlImKXkoNFAhIz0=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkobGFtYmRhMUc2IiQiK1IiUjdkIyEiKg==">JCIrUiJSN2QjISIq</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkZXJyRzYiJCIqUzw3NykhIio=">JCIqUzw3NykhIio=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkobGFtYmRhMEc2IiQiK1IiUjdkIyEiKg==">JCIrUiJSN2QjISIq</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pkkia0c2IiIiIw==">IiIj</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkZXFzRzYiNiQsKC1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSJ5R0YkNiNJInhHRiQtSSIkR0YpNiRGLiIiIyIiIiomRi4hIiItRig2JEYrRi5GM0YzKigkIis1MkY2bSEiKkYzLCZGM0YzKiQpRi5GMkYzRjVGM0YrRjNGMywqLUYoNiQtSSN5MkdGJEYtRi9GMyomRi5GNS1GKDYkRkJGLkYzRjMqKCQiK3kjeUM5JkY7RjNGPEYzRitGM0YzKihGOUYzRjxGM0ZCRjNGMw==">NiQsKC1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtRiU2JC1JInlHNiI2I0kieEdGLEYuRi4iIiIqJkYuISIiRihGL0YvKigkIis1MkY2bSEiKkYvLCZGL0YvKiQpRi4iIiNGL0YxRi9GKkYvRi8sKi1GJTYkLUYlNiQtSSN5MkdGLEYtRi5GLkYvKiZGLkYxRj1GL0YvKigkIit5I3lDOSZGNUYvRjZGL0YqRi9GLyooRjNGL0Y2Ri9GP0YvRi8=</Equation></Text-field>
</Output>
<Output>
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</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pkkkc29sRzYiZio2I0koeF9ya2Y0NUdGJDYpSSRyZXNHRiRJJWRhdGFHRiRJJXZhcnNHRiRJKXNvbG5wcm9jR0YkSSlvdXRwb2ludEdGJEkmbmRzb2xHRiRJImlHRiQ2I0lpbkNvcHlyaWdodH4oYyl+MjAwMH5ieX5XYXRlcmxvb35NYXBsZX5JbmMufkFsbH5yaWdodHN+cmVzZXJ2ZWQuR0YkRiRDKj5JOF9FbnZEU051bWVyaWNTYXZlRGlnaXRzR0YkSSdEaWdpdHNHRiQ+RjUiIzlAJS9JLV9FbnZJbkZzb2x2ZUdGJEkldHJ1ZUclKnByb3RlY3RlZEc+Ri0tJkkmZXZhbGZHRjw2I0Y0RiY+Ri0tRkBGJj5GKi1JJWV2YWxHRjw2IyZJPGRzb2x2ZS9udW1lcmljL2RhdGEvbW9kdWxlc0dJKF9zeXNsaWJHRiQ2IyIiJz5GKy1fRipJJEdldEdGJDYjUShzeXN2YXJzRiQ+RiwtRk82I1Evc29sbl9wcm9jZWR1cmVGJEAkNC1JJXR5cGVHRjw2JEYtLkkobnVtZXJpY0dGPEMkQCwtSSdtZW1iZXJHRjw2JEYnNytRJnN0YXJ0RiQuSSZzdGFydEdGJFEnbWV0aG9kRiQuSSdtZXRob2RHRiRRJWxlZnRGJFEmcmlnaHRGJFEpbGVmdGRhdGFGJFEqcmlnaHRkYXRhRiRRK2VuZ2luZWRhdGFGJEMkPkYpLUYsNiMtSShjb252ZXJ0R0Y8NiRGJy5JJ3N0cmluZ0dGPEAmLUZaNiRGKS5JJmFycmF5R0Y8Ty1GRjYkRikiIiIwRilRKXByb2NuYW1lRiRPRiktRltvNiRGJzcmUSVsYXN0RiQuSSVsYXN0R0YkUShpbml0aWFsRiQuSShpbml0aWFsR0YkQyRGam9AJC1GWjYkRikuSSVsaXN0R0Y8TzcjLUkkc2VxR0Y8NiQvJkYrNiMsJkYvRmpwRmpwRmpwJkYpRmRyL0YvOyIiISIiJTMtRlo2JEYtSSI9R0Y8LUZbbzYkLUkkbGhzR0Y8NiNGLTckRmRxRmVxQyRAJS1GWjYkLUkkcmhzR0Y8RmNzRltyPkYpLUYsNiMvRmRxNyRGaXItSSNvcEdGPDYjRmlzWVFLaW5pdGlhbH52YWx1ZXN+bXVzdH5iZX5zcGVjaWZpZWR+aW5+YX5saXN0RiRGaHEvRi1RLnNvbG5wcm9jZWR1cmVGJE8tRkY2I0YsL0YtRlJPRitAJTAlKXByb2NuYW1lR0kodW5rbm93bkdGJE8tLkZedUYmQyQ+Ri4tSShwb2ludHRvR0Y8NiMmLUZPNiNRMHNvbG5fcHJvY2VkdXJlc0YkNiNGaXJPLS5GLkYmWiVDJD5GKS1GLEZjc0ZeckYkWUYkRiRGJEYk">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</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkmeXByZWRHNiIkIjNrazNZNzwrazshI0M=">JCIza2szWTc8K2s7ISND</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkneTJwcmVkRzYiJCEzInpfLVBnJSoqM10hIz0=">JCEzInpfLVBnJSoqM10hIz0=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkobGFtYmRhMUc2IiQiK0dUTy9GISIq">JCIrR1RPL0YhIio=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkZXJyRzYiJCIkSyQhIio=">JCIkSyQhIio=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkobGFtYmRhMEc2IiQiK0dUTy9GISIq">JCIrR1RPL0YhIio=</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pkkia0c2IiIiJg==">IiIm</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L27" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">lambda0;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">JCIrR1RPL0YhIio=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L28" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">k;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">IiIm</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L29" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">err;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">JCIkSyQhIio=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L30" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">odeplot(sol,[x,y(x)],e..1,axes=boxed,thickness=3,title=&quot;Figure Exp. 3.2.32&quot;);</Text-field>
</Input>
<Output>
<Text-field style="Maple Plot" layout="Maple Plot"><Plot height="400" type="two-dimensional" width="400" plot-scale="1.0" plot-xtrans="0.0" plot-ytrans="0.0" gridlinevisibility="1" legendvisibility="false">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</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L31" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">tol:=1e-10;rho:=1/3;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkdG9sRzYiJCIiIiEjNQ==">JCIiIiEjNQ==</Equation></Text-field>
</Output>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkkcmhvRzYiIyIiIiIiJA==">IyIiIiIiJA==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L32" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">lambdaguess:=[1,5,9,13,17];</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkksbGFtYmRhZ3Vlc3NHNiI3JyIiIiIiJiIiKiIjOCIjPA==">NyciIiIiIiYiIioiIzgiIzw=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L33" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">MM:=nops(lambdaguess);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjTU1HNiIiIiY=">IiIm</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L46" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">colorlist:=[black,red,blue,yellow,green];</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkqY29sb3JsaXN0RzYiNydJJmJsYWNrR0YkSSRyZWRHRiRJJWJsdWVHRiRJJ3llbGxvd0dGJEkmZ3JlZW5HRiQ=">NydJJmJsYWNrRzYiSSRyZWRHRiRJJWJsdWVHRiRJJ3llbGxvd0dGJEkmZ3JlZW5HRiQ=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L34" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">for i from 1 to MM do </Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">lambda0:=lambdaguess[i];</Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">k:=1;err:=1;</Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">while err&gt;tol do</Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eqs:=subs(lambda=lambda0,eq),subs(lambda=lambda0,eqlambda);</Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">sol:=dsolve({eqs,ICs},{vars},type=numeric);</Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">ypred:=rhs(sol(1)[2]);</Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">y2pred:=rhs(sol(1)[4]);</Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">lambda1:=lambda0+rho*(0-ypred)/y2pred;</Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">err:=abs(lambda1-lambda0);</Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">lambda0:=lambda1;k:=k+1;</Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">end:</Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">l[i]:=lambda0;</Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">kk[i]:=k;</Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Err[i]:=err;</Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p[i]:=odeplot(sol,[x,y(x)],e..1,axes=boxed,thickness=3,color=colorlist[i]);</Text-field>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">end:</Text-field>
</Input>
</Group>
<Group labelreference="L35" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">seq(l[i],i=1..MM);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NickIitGVE8vRiEiKiQiK3k2LnptRiUkIis7ekxuNSEiKSQiKyt5NW45RiokIitOcilwJz1GKg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L36" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">seq(kk[i],i=1..MM);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NiciI2AiI14iI1giI1dGJg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L37" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">seq(Err[i],i=1..MM);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NickIiIhRiRGI0YjRiNGIw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L40" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">arw:=arrow(&lt;0.5,0.8&gt;,&lt;-0.45,-0.6&gt;,width=[1/250, relative], head_length=[0.05, relative]):
pt:=textplot([[0.8,0.95,&quot;Follow the arrow&quot;],seq([0.8,0.85-(i-1)*0.09,lambda=l[i]],i=1..MM)]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjcHRHNiItSS9JTlRFUkZBQ0VfUExPVEdGJDYoLUklVEVYVEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYkNyQkIiIpISIiJCIjJiohIiNRMUZvbGxvd350aGV+YXJyb3dGJC1GKTYkNyRGLyQiIyYpRjQvSSdsYW1iZGFHRiQkIitGVE8vRiEiKi1GKTYkNyRGLyQiI3dGNC9GPCQiK3k2LnptRj8tRik2JDckRi8kIiNuRjQvRjwkIis7ekxuNSEiKS1GKTYkNyRGLyQiI2VGNC9GPCQiKyt5NW45RlAtRik2JDckRi8kIiNcRjQvRjwkIitOcilwJz1GUA==">LSUlUExPVEc2KC1JJVRFWFRHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JDckJCIiKSEiIiQiIyYqISIjUTFGb2xsb3d+dGhlfmFycm93RiotRiY2JDckRi0kIiMmKUYyL0knbGFtYmRhR0YqJCIrRlRPL0YhIiotRiY2JDckRi0kIiN3RjIvRjokIit5Ni56bUY9LUYmNiQ3JEYtJCIjbkYyL0Y6JCIrO3pMbjUhIiktRiY2JDckRi0kIiNlRjIvRjokIisreTVuOUZOLUYmNiQ3JEYtJCIjXEYyL0Y6JCIrTnIpcCc9Rk4=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L38" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">display({seq(p[i],i=1..MM),arw,pt},title=&quot;Figure Exp.3.2.33&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, 26800 characters]</Plot></Text-field>
</Output>
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<Group labelreference="L39" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
</Worksheet>