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{SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 33 "System of ODEs -Chemical \+
Kinetics" }}{PARA 19 "" 0 "" {TEXT -1 17 "file:kinetics.mws" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 14 "with(DEtools):" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 30 "Define the system of equations" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 75 "odes := diff(x(t),t)=-k1*x(t)+kr1*y(t),diff(y(t),t
)=-(kr1+k2)*y(t)+k1*x(t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
31 "k1 := 2.0; kr1 := 4; k2 := 1.0;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 68 "Generate a direction field along with a specific solution traje
ctory" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 124 "DEplot([odes],\n[
x(t),y(t)],t=0..3.8,[ [x(0)=0.5,y(0)=2]],x=-3..3,y=-3..3,arrows=SLIM,
\ntitle=`Linear System`,linecolor=blue);" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 30 "Construct the general solution" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 27 "dsolve(\{odes\},[x(t),y(t)]):" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 24 "ics := x(0)=0.5, y(0)=0;" }}}{EXCHG {PARA 0 
"" 0 "" {TEXT -1 44 "Solve initial value problem using above ICS." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "soln := dsolve(\{odes,ics\},
[x(t),y(t)]);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 51 "Set up a procedu
re to solve the system numerically." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 65 "dsolve(\{odes,ics\},\{x(t),y(t)\},type=numeric,output
=listprocedure);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 62 "Define the so
lution as functions X(t) and Y(t) - a Maple trick" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 38 "X := subs(%,x(t)); Y := subs(%%,y(t));" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "Xplot := plot( X,0..2,color=
blue): Yplot := plot( Y,0..2,color=black):" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 30 "plots[display](\{Xplot,Yplot\});" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 29 "a := unapply(rhs(soln[2]),t);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "plot(ln(a(t)),t=0..2,labels=[\"t\",
\"log conc(x)\"],color=black);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 0 "" }}}}{MARK "0 1 0" 17 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }
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