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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 94 "This Maple Worksheet gener
ates Direction Fields for a given Differential Equation of the form " 
}{XPPEDIT 18 0 "dy/dx = f(x,y);" "6#/*&%#dyG\"\"\"%#dxG!\"\"-%\"fG6$%
\"xG%\"yG" }{TEXT -1 57 ".  Please make sure that you hit enter at the
 line below." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 127 "with(DEtoo
ls):\nDirectField:= proc(f,xstart,xend, ystart, yend)\nDEplot(diff(y(x
),x)=f,y(x),x=xstart..xend, y=ystart..yend);\nend:" }}}{EXCHG {PARA 0 
"" 0 "" {TEXT -1 45 "For example, if the Differential equation is " }
{XPPEDIT 18 0 "dy/dx = 2*x-y;" "6#/*&%#dyG\"\"\"%#dxG!\"\",&*&\"\"#F&%
\"xGF&F&%\"yGF(" }{TEXT -1 85 " and the viewing-window is x = -5..5 an
d y = -5..5, simply type the line shown below." }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 32 "DirectField(2*x-y(x),-5,5,-5,5);" }}{PARA 13 "
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{EXCHG {PARA 0 "" 0 "" {TEXT -1 192 "We may want to see particular sol
ution curves.  This can be done by specifying initial conditions.  The
 procedure below, called PartSol, draws the direction field with a sin
gle solution curve." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 172 "wit
h(DEtools):\nPartSol:= proc(f,xstart,xend, ystart, yend, xinit,yinit)
\nDEplot(diff(y(x),x)=f,y(x),x=xstart..xend, y=ystart..yend, [[y(xinit
)=yinit]], linecolor=blue);\nend:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
73 "So if one wants to add the condition y(-4) = 0, on enters the line
 below." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "PartSol(2*x-y(x)
,-5,5,-5,5,-4,0);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 13 "
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