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{SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 36 "Direction Fields and Syst
ems of ODEs" }}}{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 60 "odes := diff(x(t),t)=2*x(t)-
y(t),diff(y(t),t)=3*x(t)-2*y(t);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
68 "Generate a direction field along with a specific solution trajecto
ry" }}}{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,\nti
tle=`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)=2;" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 44 "Solve initial value problem using above ICS." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "dsolve(\{odes,ics\},[x(t),y(
t)]);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 51 "Set up a procedure to so
lve the system numerically." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
65 "dsolve(\{odes,ics\},\{x(t),y(t)\},type=numeric,output=listprocedur
e);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 62 "Define the solution as fun
ctions 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 58 "Xplot := plot( X,0..2,color=blue): \+
Yplot := plot( Y,0..2):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "
plots[display](\{Xplot,Yplot\});" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 5 "X(1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }
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