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    </Task-category>
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<Annotation-table>
    <Annotation-category name="&lt;default&gt;">
    </Annotation-category>
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<Task>
</Task>
<Group labelreference="L31" drawlabel="true">
<Input>
<Text-field style="Heading 3" italic="false" layout="Heading 3"><Font italic="false">Example 2.2.8 Multiple Steady States</Font></Text-field>
</Input>
</Group>
<Group labelreference="L32" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">restart:</Text-field>
</Input>
</Group>
<Group labelreference="L4" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">with(plots):</Text-field>
</Input>
</Group>
<Group labelreference="L34" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The governing equation is entered here:</Text-field>
</Input>
</Group>
<Group labelreference="L5" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq:=diff(theta(t),t)=P*(1-theta(t))-theta(t)*exp(-alpha*theta(t));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjZXFHNiIvLUklZGlmZkclKnByb3RlY3RlZEc2JC1JJnRoZXRhR0YkNiNJInRHRiRGLSwmKiZJIlBHRiQiIiIsJkYxRjFGKiEiIkYxRjEqJkYqRjEtSSRleHBHNiRGKEkoX3N5c2xpYkdGJDYjLCQqJkkmYWxwaGFHRiRGMUYqRjFGM0YxRjM=">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSZ0aGV0YUc2IjYjSSJ0R0YpRissJiomSSJQR0YpIiIiLCZGL0YvRichIiJGL0YvKiZGJ0YvLUkkZXhwRzYkRiVJKF9zeXNsaWJHRik2IywkKiZJJmFscGhhR0YpRi9GJ0YvRjFGL0Yx</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L35" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The steady states are found by equating the right hand side to zero:</Text-field>
</Input>
</Group>
<Group labelreference="L6" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Eq:=subs(theta(t)=theta,rhs(eq));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjRXFHNiIsJiomSSJQR0YkIiIiLCZGKEYoSSZ0aGV0YUdGJCEiIkYoRigqJkYqRigtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2IywkKiZJJmFscGhhR0YkRihGKkYoRitGKEYr">LCYqJkkiUEc2IiIiIiwmRiZGJkkmdGhldGFHRiUhIiJGJkYmKiZGKEYmLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiMsJComSSZhbHBoYUdGJUYmRihGJkYpRiZGKQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L36" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Even though P is the parameter and theta is the dependent variable, the steady state equation cannot be solved using theta as a function of P.  However, P can be solved as a function of theta as follows:</Text-field>
</Input>
</Group>
<Group labelreference="L7" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Ps:=solve(Eq,P);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkjUHNHNiIsJCooSSZ0aGV0YUdGJCIiIi1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjLCQqJkkmYWxwaGFHRiRGKEYnRighIiJGKCwmRihGMkYnRihGMkYy">LCQqKEkmdGhldGFHNiIiIiItSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2IywkKiZJJmFscGhhR0YlRiZGJEYmISIiRiYsJkYwRiZGJEYmRjBGMA==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L37" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Next, P can be plotted as a function of theta (steady state solution):</Text-field>
</Input>
</Group>
<Group labelreference="L8" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p1:=plot(subs(alpha=6,Ps),theta=0..1,view=[0..1,0..0.1],labels=[theta,P],thickness=3,title=&quot;Figure Exp. 2.2.22&quot;,axes=boxed):</Text-field>
</Input>
</Group>
<Group labelreference="L9" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p2:=plot(0.05,theta=0..1):</Text-field>
</Input>
</Group>
<Group labelreference="L41" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p3:=textplot([0.2,.055,(0.05)]):</Text-field>
</Input>
</Group>
<Group labelreference="L42" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p4:=textplot([0.58,.055,(0.05)]):</Text-field>
</Input>
</Group>
<Group labelreference="L43" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p5:=textplot([0.9,.055,(0.05)]):</Text-field>
</Input>
</Group>
<Group labelreference="L10" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">display({p1,p2,p3,p4,p5});</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">[encoded data, 8192 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L38" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">In the above plot we observe that the line P=0.05 cuts the curve at three different points.  Theta vs P can be made by using the 'implicitplot' command in Maple.</Text-field>
</Input>
</Group>
<Group labelreference="L11" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">implicitplot(P-subs(alpha=6,Ps),P=0..0.1,theta=0..0.97,thickness=3,color=green,title=&quot;Figure Exp. 2.2.23&quot;,axes=boxed);</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, 5612 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L44" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Hence, there are three different steady states.  These three different states can be obtained by equating the pressure to 0.5.</Text-field>
</Input>
</Group>
<Group labelreference="L12" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Eqtheta:=subs(alpha=6,Ps)=0.05;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkoRXF0aGV0YUc2Ii8sJCooSSZ0aGV0YUdGJCIiIi1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjLCQqJiIiJ0YpRihGKSEiIkYpLCZGKUYzRihGKUYzRjMkIiImISIj">LywkKihJJnRoZXRhRzYiIiIiLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YmNiMsJEYlISInRicsJiEiIkYnRiVGJ0YxRjEkIiImISIj</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L45" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">There are three different roots for the above equation.  They can be obtained by providing different initial guesses:</Text-field>
</Input>
</Group>
<Group labelreference="L13" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">st1:=fsolve(Eqtheta,theta=0.);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pkkkc3QxRzYiJCIrP29iPXIhIzY=">JCIrP29iPXIhIzY=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L14" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">st2:=fsolve(Eqtheta,theta=0.5);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pkkkc3QyRzYiJCIrNDZteVwhIzU=">JCIrNDZteVwhIzU=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L15" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">st3:=fsolve(Eqtheta,theta=0.8);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pkkkc3QzRzYiJCIrKHowdUgqISM1">JCIrKHowdUgqISM1</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L46" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Next, the transient equation is solved for different initial conditions:</Text-field>
</Input>
</Group>
<Group labelreference="L16" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eqtheta:=subs(alpha=6,P=0.05,eq);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="PkkoZXF0aGV0YUc2Ii8tSSVkaWZmRyUqcHJvdGVjdGVkRzYkLUkmdGhldGFHRiQ2I0kidEdGJEYtLCgkIiImISIjIiIiKiZGL0YyRipGMiEiIiomRipGMi1JJGV4cEc2JEYoSShfc3lzbGliR0YkNiMsJComIiInRjJGKkYyRjRGMkY0">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSZ0aGV0YUc2IjYjSSJ0R0YpRissKCQiIiYhIiMiIiJGJyQhIiZGLyomRidGMC1JJGV4cEc2JEYlSShfc3lzbGliR0YpNiMsJEYnISInRjAhIiI=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L17" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">sol:=dsolve({eqtheta,theta(0)=0},theta(t),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="L18" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">odeplot(sol,[t,theta(t)],0.0..20,axes=boxed,color=blue,title&quot;Figure Exp. 2.2.24&quot;,thickness=3);</Text-field>
</Input>
<Output>
<Text-field style="Error" layout="Error">Error, unexpected string</Text-field>
</Output>
</Group>
<Group labelreference="L19" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">sol:=dsolve({eqtheta,theta(0)=1},theta(t),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="L20" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">odeplot(sol,[t,theta(t)],0.0..500,axes=boxed,color=magenta,title=&quot;Figure Exp. 2.2.25&quot;,thickness=3);</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">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</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L21" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">sol:=dsolve({eqtheta,theta(0)=0.5},theta(t),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="L22" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">odeplot(sol,[t,theta(t)],0.0..500,axes=boxed,title=&quot;Figure Exp. 2.2.26&quot;,thickness=3);</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">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</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L23" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">sol:=dsolve({eqtheta,theta(0)=0.4},theta(t),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="L24" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">odeplot(sol,[t,theta(t)],0.0..50,axes=boxed,color=green,title=&quot;Figure 2.2.27,&quot;thickness=3);</Text-field>
</Input>
<Output>
<Text-field style="Error" layout="Error">Error, missing operator or `;`</Text-field>
</Output>
</Group>
<Group labelreference="L47" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">We obtained three different steady states.  The stability of these states can be verified by assigning these values as the initial conditions.  If we start with a stable steady state solution as the initial condition, the process remains at the stable steady state solution.  If we start with an unstable steady state solution, the process moves to one of the steady state solutions.</Text-field>
</Input>
</Group>
<Group labelreference="L25" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">sol:=dsolve({eqtheta,theta(0)=st1},theta(t),type=numeric);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="Pkkkc29sRzYiZio2I0koeF9ya2Y0NUdGJDYpSSRyZXNHRiRJJWRhdGFHRiRJJXZhcnNHRiRJKXNvbG5wcm9jR0YkSSlvdXRwb2ludEdGJEkmbmRzb2xHRiRJImlHRiQ2I0lpbkNvcHlyaWdodH4oYyl+MjAwMH5ieX5XYXRlcmxvb35NYXBsZX5JbmMufkFsbH5yaWdodHN+cmVzZXJ2ZWQuR0YkRiRDKj5JOF9FbnZEU051bWVyaWNTYXZlRGlnaXRzR0YkSSdEaWdpdHNHRiQ+RjUiIzlAJS9JLV9FbnZJbkZzb2x2ZUdGJEkldHJ1ZUclKnByb3RlY3RlZEc+Ri0tJkkmZXZhbGZHRjw2I0Y0RiY+Ri0tRkBGJj5GKi1JJWV2YWxHRjw2IyZJPGRzb2x2ZS9udW1lcmljL2RhdGEvbW9kdWxlc0dJKF9zeXNsaWJHRiQ2IyIiJj5GKy1fRipJJEdldEdGJDYjUShzeXN2YXJzRiQ+RiwtRk82I1Evc29sbl9wcm9jZWR1cmVGJEAkNC1JJXR5cGVHRjw2JEYtLkkobnVtZXJpY0dGPEMkQCwtSSdtZW1iZXJHRjw2JEYnNytRJnN0YXJ0RiQuSSZzdGFydEdGJFEnbWV0aG9kRiQuSSdtZXRob2RHRiRRJWxlZnRGJFEmcmlnaHRGJFEpbGVmdGRhdGFGJFEqcmlnaHRkYXRhRiRRK2VuZ2luZWRhdGFGJEMkPkYpLUYsNiMtSShjb252ZXJ0R0Y8NiRGJy5JJ3N0cmluZ0dGPEAmLUZaNiRGKS5JJmFycmF5R0Y8Ty1GRjYkRikiIiIwRilRKXByb2NuYW1lRiRPRiktRltvNiRGJzcmUSVsYXN0RiQuSSVsYXN0R0YkUShpbml0aWFsRiQuSShpbml0aWFsR0YkQyRGam9AJC1GWjYkRikuSSVsaXN0R0Y8TzcjLUkkc2VxR0Y8NiQvJkYrNiMsJkYvRmpwRmpwRmpwJkYpRmRyL0YvOyIiIUZqcDMtRlo2JEYtSSI9R0Y8LUZbbzYkLUkkbGhzR0Y8NiNGLTckRmRxRmVxQyRAJS1GWjYkLUkkcmhzR0Y8RmJzRltyPkYpLUYsNiMvRmRxNyRGaXItSSNvcEdGPDYjRmhzWVFLaW5pdGlhbH52YWx1ZXN+bXVzdH5iZX5zcGVjaWZpZWR+aW5+YX5saXN0RiRGaHEvRi1RLnNvbG5wcm9jZWR1cmVGJE8tRkY2I0YsL0YtRlJPRitAJTAlKXByb2NuYW1lR0kodW5rbm93bkdGJE8tLkZddUYmQyQ+Ri4tSShwb2ludHRvR0Y8NiMmLUZPNiNRMHNvbG5fcHJvY2VkdXJlc0YkNiNGaXJPLS5GLkYmWiVDJD5GKS1GLEZic0ZeckYkWUYkRiRGJEYk">Zio2I0koeF9ya2Y0NUc2IjYpSSRyZXNHRiVJJWRhdGFHRiVJJXZhcnNHRiVJKXNvbG5wcm9jR0YlSSlvdXRwb2ludEdGJUkmbmRzb2xHRiVJImlHRiU2I0lpbkNvcHlyaWdodH4oYyl+MjAwMH5ieX5XYXRlcmxvb35NYXBsZX5JbmMufkFsbH5yaWdodHN+cmVzZXJ2ZWQuR0YlRiVDKj5JOF9FbnZEU051bWVyaWNTYXZlRGlnaXRzR0YlSSdEaWdpdHNHRiU+RjMiIzlAJS9JLV9FbnZJbkZzb2x2ZUdGJUkldHJ1ZUclKnByb3RlY3RlZEc+OCgtJkkmZXZhbGZHRjo2I0YyNiM5JD5GPC1GP0ZBPjglLUklZXZhbEdGOjYjJkk8ZHNvbHZlL251bWVyaWMvZGF0YS9tb2R1bGVzR0koX3N5c2xpYkdGJTYjIiImPjgmLV9GRkkkR2V0R0YlNiNRKHN5c3ZhcnNGJT44Jy1GUjYjUS9zb2xuX3Byb2NlZHVyZUYlQCQ0LUkldHlwZUdGOjYkRjwuSShudW1lcmljR0Y6QyRALC1JJ21lbWJlckdGOjYkRkI3K1Emc3RhcnRGJS5JJnN0YXJ0R0YlUSdtZXRob2RGJS5JJ21ldGhvZEdGJVElbGVmdEYlUSZyaWdodEYlUSlsZWZ0ZGF0YUYlUSpyaWdodGRhdGFGJVErZW5naW5lZGF0YUYlQyQ+OCQtRlc2Iy1JKGNvbnZlcnRHRjo2JEZCLkknc3RyaW5nR0Y6QCYtRmhuNiRGX3AuSSZhcnJheUdGOk8tRkg2JEZfcCIiIjBGX3BRKXByb2NuYW1lRiVPRl9wLUZfbzYkRkI3JlElbGFzdEYlLkklbGFzdEdGJVEoaW5pdGlhbEYlLkkoaW5pdGlhbEdGJUMkRl5wQCQtRmhuNiRGX3AuSSVsaXN0R0Y6TzcjLUkkc2VxR0Y6NiQvJkZQNiMsJjgqRl9xRl9xRl9xJkZfcEZpci9GW3M7IiIhRl9xMy1GaG42JEY8SSI9R0Y6LUZfbzYkLUkkbGhzR0Y6NiNGPDckRmlxRmpxQyRAJS1GaG42JC1JJHJoc0dGOkZoc0Zgcj5GX3AtRlc2Iy9GaXE3JEZfcy1JI29wR0Y6NiNGXnRZUUtpbml0aWFsfnZhbHVlc35tdXN0fmJlfnNwZWNpZmllZH5pbn5hfmxpc3RGJUZdci9GPFEuc29sbnByb2NlZHVyZUYlTy1GSDYjRlcvRjxGVU9GUEAlMDkhSSh1bmtub3duR0YlTy0uRmN1RkFDJD44KS1JKHBvaW50dG9HRjo2IyYtRlI2I1Ewc29sbl9wcm9jZWR1cmVzRiU2I0Zfc08tLkZqdUZBWiVDJD5GX3AtRldGaHNGY3JGJVlGJUYlRiVGJQ==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L26" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">odeplot(sol,[t,theta(t)],0..1000,axes=boxed,color=blue,title=&quot;Figure Exp. 2.2.28&quot;,thickness=3,view=[0..1000,0..1]);</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">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</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L27" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">sol:=dsolve({eqtheta,theta(0)=st3},theta(t),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="L28" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">odeplot(sol,[t,theta(t)],0.0..1000,axes=boxed,color=magenta,title=&quot;Figure Exp. 2.2.9&quot;,thickness=3,view=[0..1000,0..1]);</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">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</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L29" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">sol:=dsolve({eqtheta,theta(0)=st2},theta(t),type=numeric);</Text-field>
</Input>
<Output>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">odeplot(sol,[t,theta(t)],0.0..1000,axes=boxed,title=&quot;Figure Exp. 2.2.30&quot;,thickness=3);</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">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</Plot></Text-field>
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<Text-field style="Text" layout="Normal">We observe that both st1=0.071 and st3=0.93 are stable steady states.  However, st2=0.498 is an unstable steady state.  The dependent variable stays at st2 only until t=400 and then the process approaches the stable steady state st3.</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal"></Text-field>
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