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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT -1 15 "Phase portraits" }}
{PARA 0 "" 0 "" {TEXT 256 30 "To plot a graph of x against t" }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 77 "First load the \+
algebraic and graphics packages linalg and  DEtools as follows" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}{PARA 7 "" 
1 "" {TEXT -1 32 "Warning, new definition for norm" }}{PARA 7 "" 1 "" 
{TEXT -1 33 "Warning, new definition for trace" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 14 "with(DEtools):" }}{PARA 7 "" 1 "" {TEXT -1 35 
"Warning, new definition for adjoint" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 68 "Next enter the differential equations. The commands are shown b
elow." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "A:=diff(x(t),t)=y;
" }}{PARA 11 "" 1 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 23 "B:=diff(y(t),t)=-x-2*y;" }}{PARA 11 "" 1 "" {TEXT -1 
0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 124 "Now write the command for
 the plot. this is very similar to the phase plot except that there is
 one extra term \"scene=[t,x]\"" }}{PARA 0 "" 0 "" {TEXT -1 58 "the tr
ajectory plotted is the one through the point (0,4)." }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 94 "DEplot([A,B],[x(t),y(t)],-2..5,[[x(0)=0,y(0)=4]],x=-5..5,y=-5..5
,scene=[t,x],linecolor=black);" }}{PARA 13 "" 1 "" {TEXT -1 0 "" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 49 "Try changing the initial value and
 the range of t" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}
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