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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT 256 16 "Phase portraits " }}
{PARA 0 "" 0 "" {TEXT 257 34 "To plot a direction field diagram " }
{TEXT -1 14 "for the system" }}{PARA 256 "" 0 "" {OLE 1 4097 1 "[xm]Br
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:::::::::::::4:" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 77 "First load the algebraic and graphics pac
kages linalg and  DEtools as follows" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 13 "with(linalg):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 14 "with(DEtools):" }}{PARA 7 "" 1 "" {TEXT -1 35 "Warning, new de
finition for adjoint" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 68 "Next ente
r the differential equations. The commands are shown below." }}}
{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 39 "Finally write the command for the plot." 
}}{PARA 0 "" 0 "" {TEXT -1 81 "Note that the range -2..5 is the range \+
of t, the x and y ranges are explanatory. " }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 64 "DEplot([A,B],[x(t),y(t)],-2..5,x=-5..5,y=-5..5,line
color=black);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}}{MARK "0 0 \+
0" 15 }{VIEWOPTS 1 1 0 1 1 1803 }