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<Text-field style="Heading 2" layout="Heading 2">2.2 Nonlinear Ordinary Differential Equations</Text-field>
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<Text-field style="Heading 3" italic="false" layout="Heading 3"><Font italic="false">Example 2.2.1 Simultaneous Series Reactions</Font></Text-field>
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<Text-field style="Text" layout="Normal">Consider a second order reaction</Text-field>
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<Text-field style="Text" layout="Normal">governed by the nonlinear ODEs:</Text-field>
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<Text-field style="Text" layout="Normal" alignment="centred"><Equation executable="false" style="Text" input-equation="" display="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">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</Equation>= <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW9HRiQ2LVEqJnVtaW51czA7RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRkMtRiw2LVEifkYnRi9GMkY1RjdGOUY7Rj1GPy9GQlEmMC4wZW1GJy9GRUZKLUkobXN1YnN1cEdGJDYnLUYjNiYtSSNtaUdGJDYlUSJrRicvJSdpdGFsaWNHRjRGLy1GUjYmUSIxRidGVS8lKnN1YnNjcmlwdEdRJXRydWVGJ0YvLUZSNiVRImNGJ0ZVRi9GLy1GIzYkLUZSNiVRImFGJ0ZVRi9GLy1GIzYkLUkjbW5HRiQ2JFEiMkYnRi9GLy8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRicvJS9zdWJzY3JpcHRzaGlmdEdGZ29GRkYv">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</Equation></Text-field>
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<Text-field style="Text" layout="Normal" alignment="centred"><Equation executable="false" style="Text" input-equation="" display="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">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkmbWZyYWNHRiQ2KC1GIzYmLUkjbW9HRiQ2LVEwJkRpZmZlcmVudGlhbEQ7RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZ1bnNldEYnLyUqc2VwYXJhdG9yR0Y5LyUpc3RyZXRjaHlHRjkvJSpzeW1tZXRyaWNHRjkvJShsYXJnZW9wR0Y5LyUubW92YWJsZWxpbWl0c0dGOS8lJ2FjY2VudEdGOS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkgtSSNtaUdGJDYlUSJjRicvJSdpdGFsaWNHUSZmYWxzZUYnRjQtRkw2JlEiYkYnRk8vJSpzdWJzY3JpcHRHUSV0cnVlRidGNEY0LUYjNiVGMC1GTDYlUSJ0RidGT0Y0RjQvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRlxvLyUpYmV2ZWxsZWRHRlEtRkw2I1EhRidGNA==</Equation>= <Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYrLUkjbW9HRiQ2LVEqJnVtaW51czA7RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRkMtSShtc3Vic3VwR0YkNictRiM2Ji1JI21pR0YkNiVRImtGJy8lJ2l0YWxpY0dGNEYvLUZMNiZRIjFGJ0ZPLyUqc3Vic2NyaXB0R1EldHJ1ZUYnRi8tRkw2JVEiY0YnRk9GL0YvLUYjNiQtRkw2JVEiYkYnRk9GL0YvLUYjNiQtSSNtbkdGJDYkUSIyRidGL0YvLyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy8lL3N1YnNjcmlwdHNoaWZ0R0Zhby1GLDYtUSJ+RidGL0YyRjVGN0Y5RjtGPUY/L0ZCUSYwLjBlbUYnL0ZFRmhvRitGSy1GTDYmRl5vRk9GVEYvRlctRkw2JkZobkZPRlRGL0Yv">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYrLUkjbW9HRiQ2LVEqJnVtaW51czA7RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRkMtSShtc3Vic3VwR0YkNictRiM2Ji1JI21pR0YkNiVRImtGJy8lJ2l0YWxpY0dGNEYvLUZMNiZRIjFGJ0ZPLyUqc3Vic2NyaXB0R1EldHJ1ZUYnRi8tRkw2JVEiY0YnRk9GL0YvLUYjNiQtRkw2JVEiYkYnRk9GL0YvLUYjNiQtSSNtbkdGJDYkUSIyRidGL0YvLyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy8lL3N1YnNjcmlwdHNoaWZ0R0Zhby1GLDYtUSJ+RidGL0YyRjVGN0Y5RjtGPUY/L0ZCUSYwLjBlbUYnL0ZFRmhvRitGSy1GTDYmRl5vRk9GVEYvRlctRkw2JkZobkZPRlRGL0Yv</Equation></Text-field>
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<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal">with the initial conditions ca(0) = 1; cb(0) = 0 and  cc(0) = 0; and, k1 and k2  are the rate constants.  The concentration of species C(cc) at any time is given by the material balance</Text-field>
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<Text-field style="Text" layout="Normal" alignment="centred">ca + cb + cc = ca(0) = 1</Text-field>
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<Text-field style="Text" layout="Normal">The equation above is solved below in Maple:</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">restart:</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">with(plots):</Text-field>
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<Text-field style="Text" layout="Normal">The governing equations are entered here:</Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq[1]:=diff(ca(t),t)=-k1*ca(t)^2;</Text-field>
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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSNjYUc2IjYjSSJ0R0YpRissJComSSNrMUdGKSIiIilGJyIiI0YvISIi</Equation></Text-field>
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<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eq[2]:=diff(cb(t),t)=k1*ca(t)^2-k2*cb(t);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">Ly1JJWRpZmZHJSpwcm90ZWN0ZWRHNiQtSSNjYkc2IjYjSSJ0R0YpRissJiomSSNrMUdGKSIiIiktSSNjYUdGKUYqIiIjRi9GLyomSSNrMkdGKUYvRidGLyEiIg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L15" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The variables are entered here:</Text-field>
</Input>
</Group>
<Group labelreference="L16" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">vars:=(ca(t),cb(t));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">NiQtSSNjYUc2IjYjSSJ0R0YlLUkjY2JHRiVGJg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L17" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The equations are stored in eqs.</Text-field>
</Input>
</Group>
<Group labelreference="L18" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">eqs:=(eq[1],eq[2]);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">NiQvLUklZGlmZkclKnByb3RlY3RlZEc2JC1JI2NhRzYiNiNJInRHRipGLCwkKiZJI2sxR0YqIiIiKUYoIiIjRjAhIiIvLUYlNiQtSSNjYkdGKkYrRiwsJkYuRjAqJkkjazJHRipGMEY3RjBGMw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L19" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The initial conditions are stored in ICs:</Text-field>
</Input>
</Group>
<Group labelreference="L20" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">ICs:=(ca(0)=1,cb(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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">NiQvLUkjY2FHNiI2IyIiISIiIi8tSSNjYkdGJkYnRig=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L21" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">sol:=dsolve({eqs,ICs},{vars});</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">PCQvLUkjY2FHNiI2I0kidEdGJiokLCYqJkkjazFHRiYiIiJGKEYtRi1GLUYtISIiLy1JI2NiR0YmRicqJiwmKihGLEYuSSNrMkdGJkYtLCYqJi1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJjYjKiZGNUYtRihGLUYtLCZGPkYtKiZGLEYuRjVGLUYtRi5GLiomLUY5NiMsJEZARi5GLS1JI0VpR0Y6NiRGLSwmRj5GLkZARi5GLUYuRi1GLSooLCYqJkYsRi0tRjk2I0ZARi1GLSomLUZGNiRGLUZERi1GNUYtRi1GLUYsRi5GTEYuRi1GLS1GOTYjLCRGPkYuRi0=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L22" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">assign(sol):</Text-field>
</Input>
</Group>
<Group labelreference="L23" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">ca(t);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KiQsJiomSSNrMUc2IiIiIkkidEdGJkYnRidGJ0YnISIi</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L24" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">cb(t);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KiYsJiooSSNrMUc2IiEiIkkjazJHRiYiIiIsJiomLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YmNiMqJkYoRilJInRHRiZGKUYpLCZGMkYpKiZGJUYnRihGKUYpRidGJyomLUYtNiMsJEY1RidGKS1JI0VpR0YuNiRGKSwmRjJGJ0Y1RidGKUYnRilGKSooLCYqJkYlRiktRi02I0Y1RilGKSomLUY7NiRGKUY5RilGKEYpRilGKUYlRidGQUYnRilGKS1GLTYjLCRGMkYnRik=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L25" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The help command in Maple is invoked to describe Ei.  The following description for Ei is given in Maple's help file.</Text-field>
</Input>
</Group>
<Group labelreference="L26" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">?Ei</Text-field>
</Input>
</Group>
<Group labelreference="L27" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"></Text-field>
<Text-field style="Text" layout="Normal">Ei - The Exponential Integral</Text-field>
<Text-field style="Text" layout="Normal">Calling Sequence</Text-field>
<Text-field style="Text" layout="Normal">     Ei(z)</Text-field>
<Text-field style="Text" layout="Normal">     Ei(a, z)</Text-field>
<Text-field style="Text" layout="Normal">Parameters</Text-field>
<Text-field style="Text" layout="Normal">     z - algebraic expression</Text-field>
<Text-field style="Text" layout="Normal">     a - algebraic expression</Text-field>
<Text-field style="Text" layout="Normal">Description</Text-field>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">\342\200\242  The exponential integrals, Ei(a, z), are defined for Re(z) &gt; 0 by </Font></Text-field>
<Text-field style="Text" layout="Normal">&gt; Ei(a, z) = convert(Ei(a, z), Int) assuming Re(z) &gt; 0;</Text-field>
<Text-field style="Text" layout="Normal"> </Text-field>
<Text-field style="Text" layout="Normal">This classical definition is extended by analytic continuation to the entire complex plane using </Text-field>
<Text-field style="Text" layout="Normal">&gt; Ei(a, z) = z^(a-1)*GAMMA(1-a, z);</Text-field>
<Text-field style="Text" layout="Normal"> </Text-field>
<Text-field style="Text" layout="Normal">with the exception of the point 0 in the case of Ei(1, z). </Text-field>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">\342\200\242  For all of these functions, 0 is a branch point and the negative real axis is the branch cut. The values on the branch cut are assigned such that the functions are continuous in the direction of increasing argument (equivalently, from above). </Font></Text-field>
<Text-field style="Text" layout="Normal"><Font encoding="UTF-8">\342\200\242  The classical definition for the 1-argument exponential integral is a Cauchy Principal Value integral, defined for real arguments x, as the following </Font></Text-field>
<Text-field style="Text" layout="Normal">&gt; convert(Ei(x),Int) assuming x::real;</Text-field>
<Text-field style="Text" layout="Normal"> </Text-field>
<Text-field style="Text" layout="Normal">&gt; value(%);</Text-field>
<Text-field style="Text" layout="Normal"> </Text-field>
<Text-field style="Text" layout="Normal">for x &lt; 0, Ei(x) = -Ei(1, -x). This classical definition is extended to the entire complex plane using </Text-field>
<Text-field style="Text" layout="Normal" alignment="centred">Ei(z) = -Ei(1, -z) + (ln(z) - ln(1/z))/2 - ln(-z)</Text-field>
<Text-field style="Text" layout="Normal">Note that this extension has its branch cut on the negative real axis, but unlike for the 2-argument Ei functions this extension is not continuous onto the branch cut from either above or below. That is, this extension provides an analytic continuation of Ei(z) from the positive real axis, but not in any direction from the negative real axis. If you want a continuation from the negative real axis, use -Ei(1, -z) in place of Ei(z). </Text-field>
<Text-field style="Text" layout="Normal">Reference:</Text-field>
<Text-field style="Text" layout="Normal">Abramowitz, M. and Stegun, I. Handbook of Mathematical Functions. New York: Dover Publications Inc., 1965.</Text-field>
<Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group>
<Group labelreference="L28" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The concentration of species C is found using the material balance.</Text-field>
</Input>
</Group>
<Group labelreference="L29" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">cc(t):=1-ca(t)-cb(t);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUYjNictSSNtaUdGJDYlUSNjY0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RMCZBcHBseUZ1bmN0aW9uO0YnL0Y1USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPy8lKXN0cmV0Y2h5R0Y/LyUqc3ltbWV0cmljR0Y/LyUobGFyZ2VvcEdGPy8lLm1vdmFibGVsaW1pdHNHRj8vJSdhY2NlbnRHRj8vJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZOLUkobWZlbmNlZEdGJDYkLUYjNiUtRi42JVEidEYnRjFGNC8lK2ZvcmVncm91bmRHUShbMCwwLDBdRidGO0Y7RllGOy1GODYtUSM6PUYnRjtGPUZARkJGREZGRkhGSi9GTVEsMC4yNzc3Nzc4ZW1GJy9GUEZqbi1GIzYoLUkjbW5HRiQ2JFEiMUYnRjstRjg2LVEoJm1pbnVzO0YnRjtGPUZARkJGREZGRkhGSi9GTVEsMC4yMjIyMjIyZW1GJy9GUEZmby1JJm1mcmFjR0YkNihGXm8tRiM2JS1GIzYmLUYjNiYtRi42JVEjazFGJ0YxRjQtRjg2LVExJkludmlzaWJsZVRpbWVzO0YnRjtGPUZARkJGREZGRkhGSkZMRk9GVkY7LUY4Ni1RIitGJ0Y7Rj1GQEZCRkRGRkZIRkpGZW9GZ29GXm9GO0ZZRjsvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRl9xLyUpYmV2ZWxsZWRHRj9GYm8tRiM2Ji1GUjYkLUYjNiYtRmlvNigtRiM2Jy1GLjYlUSNrMkYnRjFGNEZkcC1GUjYkLUYjNictRjg2LVEqJnVtaW51czA7RidGO0Y9RkBGQkZERkZGSEZKRmVvRmdvLUZpbzYoLUYjNiUtSSVtc3VwR0YkNiUtRjg2LVEvJkV4cG9uZW50aWFsRTtGJ0Y7Rj1GQEZCRkRGRkZIRkpGTC9GUFEsMC4xMTExMTExZW1GJy1GIzYmRl5yRmRwRlZGOy8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGWUY7LUYjNiUtRiM2JkZkc0ZncC1GaW82KC1GIzYlRl5yRllGOy1GIzYlRmFwRllGO0ZqcEZdcUZgcUZicUY7RllGO0ZqcEZdcUZgcUZicUZiby1GIzYmLUZdczYlRl9zLUYjNiZGZXJGXXRGWUY7RmZzRmRwLUYjNictRi42JVEjRWlGJy9GMkY/RjtGNy1GUjYkLUYjNidGXm8tRjg2LVEiLEYnRjtGPS9GQUYzRkJGREZGRkhGSkZML0ZQUSwwLjMzMzMzMzNlbUYnLUYjNidGZXJGZHNGYm9GXXRGO0ZZRjtGO0ZZRjtGO0Y7RjtGWUY7RmF0RmpwRl1xRmBxRmJxRmdwLUZpbzYoLUYjNiUtRiM2Ji1GIzYmRmFwRmRwLUZdczYlRl9zRl10RmZzRjtGZ3AtRiM2Ji1GIzYnRlt1RjctRlI2JC1GIzYnRl5vRmN1Rmd0RllGO0Y7RllGO0ZkcEZeckY7RjtGWUY7LUYjNidGYXBGZHBGY3ZGWUY7RmpwRl1xRmBxRmJxRjtGO0ZkcC1GXXM2JUZfcy1GIzYmRmVyRmRzRllGO0Zmc0Y7RjtGWUY7">LCgiIiJGIyokLCYqJkkjazFHNiJGI0kidEdGKEYjRiNGI0YjISIiRioqJiwmKihGJ0YqSSNrMkdGKEYjLCYqJi1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGKDYjKiZGLkYjRilGI0YjLCZGN0YjKiZGJ0YqRi5GI0YjRipGKiomLUYyNiMsJEY5RipGIy1JI0VpR0YzNiRGIywmRjdGKkY5RipGI0YqRiNGIyooLCYqJkYnRiMtRjI2I0Y5RiNGIyomLUY/NiRGI0Y9RiNGLkYjRiNGI0YnRipGRUYqRiNGIy1GMjYjLCRGN0YqRiNGKg==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L30" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Plots can be made for different values of rate constants.</Text-field>
</Input>
</Group>
<Group labelreference="L31" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group>
<Group labelreference="L32" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group>
<Group labelreference="L33" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">pars:={k1=1,k2=1};</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">PCQvSSNrMkc2IiIiIi9JI2sxR0YlRiY=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L34" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Ca:=subs(pars,ca(t));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KiQsJkkidEc2IiIiIkYmRiYhIiI=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L35" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Cb:=subs(pars,cb(t));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KiYsKComLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJInRHRioiIiIsJkYsRi1GLUYtISIiRi8qJi1GJjYjRi9GLS1JI0VpR0YnNiRGLSwmRixGL0YtRi9GLUYvKiYsJi1GJjYjRi1GLS1GNDYkRi1GL0YtRi1GOUYvRi1GLS1GJjYjLCRGLEYvRi0=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L36" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Cc:=subs(pars,cc(t));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCgiIiJGIyokLCZJInRHNiJGI0YjRiMhIiJGKComLCgqJi1JJGV4cEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJzYjRiZGI0YlRihGKComLUYtNiNGKEYjLUkjRWlHRi42JEYjLCZGJkYoRiNGKEYjRigqJiwmLUYtNiNGI0YjLUY2NiRGI0YoRiNGI0Y7RihGI0YjLUYtNiMsJEYmRihGI0Yo</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L37" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p1:=plot(eval(Ca),t=0..10,thickness=4):</Text-field>
</Input>
</Group>
<Group labelreference="L38" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p2:=plot(eval(Re(Cb)),t=0..10,linestyle=1,color=green,thickness=4,axes=boxed):</Text-field>
</Input>
</Group>
<Group labelreference="L39" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p3:=plot(eval(Re(Cc)),t=0..10,linestyle=4,thickness=4,color=gold):</Text-field>
</Input>
</Group>
<Group labelreference="L40" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">To get rid of the residual errors while calculating the Ei functions only the real part is plotted.</Text-field>
</Input>
</Group>
<Group labelreference="L41" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">display({p1,p2,p3},labels=[t,C],title=&quot;Figure Exp. 2.2.1&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">[encoded data, 8588 characters]</Plot></Text-field>
</Output>
</Group>
<Group labelreference="L42" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">pars:={k1=2,k2=1};</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">PCQvSSNrMUc2IiIiIy9JI2syR0YlIiIi</Equation></Text-field>
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<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Ca:=subs(pars,ca(t));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KiQsJiomIiIjIiIiSSJ0RzYiRiZGJkYmRiYhIiI=</Equation></Text-field>
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<Group labelreference="L44" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Cb:=subs(pars,cb(t));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">KiYsKCooIyIiIiIiI0YmLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJInRHRi1GJiwmRi9GJkYlRiYhIiJGMSooRiVGJi1GKTYjI0YxRidGJi1JI0VpR0YqNiRGJiwmRi9GMUYlRjFGJkYxKihGJUYmLCYqJkYnRiYtRik2I0YlRiZGJi1GNzYkRiZGNUYmRiZGPUYxRiZGJi1GKTYjLCRGL0YxRiY=</Equation></Text-field>
</Output>
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<Group labelreference="L45" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">Cc:=subs(pars,cc(t));</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LCgiIiJGIyokLCYqJiIiI0YjSSJ0RzYiRiNGI0YjRiMhIiJGKiomLCgqKCNGI0YnRiMtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRik2I0YoRiMsJkYoRiNGLkYjRipGKiooRi5GIy1GMDYjI0YqRidGIy1JI0VpR0YxNiRGIywmRihGKkYuRipGI0YqKihGLkYjLCYqJkYnRiMtRjA2I0YuRiNGIy1GOzYkRiNGOUYjRiNGQUYqRiNGIy1GMDYjLCRGKEYqRiNGKg==</Equation></Text-field>
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<Group labelreference="L46" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p1:=plot(Ca,t=0..10,thickness=4):</Text-field>
</Input>
</Group>
<Group labelreference="L47" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p2:=plot(Re(Cb),t=0..10,linestyle=1,thickness=4,color=green,axes=boxed):</Text-field>
</Input>
</Group>
<Group labelreference="L48" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">p3:=plot(Re(Cc),t=0..10,linestyle=4,thickness=4,color=gold):</Text-field>
</Input>
</Group>
<Group labelreference="L49" drawlabel="true">
<Input>
<Text-field prompt="&gt; " style="Maple Input" layout="Normal">display({p1,p2,p3},labels=[t,C],title=&quot;Figure Exp. 2.2.2&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">[encoded data, 8596 characters]</Plot></Text-field>
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<Group labelreference="L50" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">We observe that a maximum exists for the concentration of species B.  Sometimes, Maple gives implicit solutions, i.e., independent variable (t), as a function of the dependent variable (y).</Text-field>
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<Input>
<Text-field prompt="&gt; " style="Normal" layout="Normal"></Text-field>
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