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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 91 " t1_prob4_ANS_A10.mws\nMon
 Oct 10 09:45:25 MDT 2005\n\nA Maple solution to problem 4, Test #1." 
}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 30 "The pro
blem was to sketch the " }{XPPEDIT 18 0 "m = -1;" "6#/%\"mG,$\"\"\"!\"
\"" }{TEXT -1 2 ", " }{XPPEDIT 18 0 "m = 0;" "6#/%\"mG\"\"!" }{TEXT 
-1 6 ", and " }{XPPEDIT 18 0 "m = 1;" "6#/%\"mG\"\"\"" }{TEXT -1 41 " \+
isoclines, the direction field, and the " }{XPPEDIT 18 0 "y(-1) = -1;
" "6#/-%\"yG6#,$\"\"\"!\"\",$F(F)" }{TEXT -1 10 " solution " }}{PARA 
0 "" 0 "" {TEXT -1 47 "for the differential equation y' = t - y^2 + 2.
" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 
"with(plots, display, implicitplot, textplot);" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 22 "with(DEtools, DEplot);" }}}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 60 "####################
########################################" }}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}{PARA 0 "" 0 "" {TEXT -1 54 "Plot ranges, the RHS function, and
 the list of slopes:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 27 "TRG := -5..4: YRG := -3..3:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "RHS := (t,y) -> t - y^2 + 2;" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "mLIST := [-1,0,1]; " }{TEXT 
-1 20 "Slopes for isoclines" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }
}{PARA 0 "" 0 "" {TEXT -1 38 "######################################" 
}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 48 "Here's \+
a Maple procedure which, given the slope " }{XPPEDIT 18 0 "u;" "6#%\"u
G" }{TEXT -1 56 ", produces a labeled plot of the corresponding isocli
ne." }}{PARA 0 "" 0 "" {TEXT -1 1 " " }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 17 "utah := proc(u)  " }{TEXT -1 25 "slope -> labeled iso
cline" }{MPLTEXT 1 0 264 "\n local tm, ym, us;\n tm := op(2, TRG);\n y
m := sort(evalf([solve(RHS(tm,y)=u,y)]))[2];\n us := convert(u, 'strin
g'):  us := \"m = \"||us:\n implicitplot(RHS(t,y)=u, t=TRG, y=YRG,    \+
    colour=BLACK,grid=[75,75]),\n   textplot([tm+1/5,ym, us], align=\{
ABOVE,RIGHT\}):\nend;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 62 "#########################################
#####################" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 
"" {TEXT -1 69 "Now \"map\" and \"utah\" generate the list of plots of
 labeled isoclines." }}{PARA 0 "" 0 "" {TEXT -1 1 " " }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 34 "isoclineLIST := map(utah, mLIST): " }
{TEXT -1 18 "Plots of isoclines" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 22 "P := op(isoclineLIST):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 0 "" 0 "" {TEXT -1 61 "#####################################
########################" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "
" 0 "" {TEXT -1 128 "Now we set up the differential equation and the y
(-1) = -1 initial condition to plot the direction field and the soluti
on curve." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 30 "DE := D(y)(t) = RHS(t, y(t)); " }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 13 "VAR := y(t): " }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 21 "INIT := [[y(-1)=-1]]:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 55 "P := P, DEplot(DE,VAR,t=TRG,INIT,y=YRG, stepsize=0.05
):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 63 "###############################################################
" }}{PARA 0 "" 0 "" {TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 71 "Prod
uce a plot with isoclines, direction field, and the solution curve:" }
}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 13 "display([P]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "####
###################################" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}}{MARK "22" 0 }{VIEWOPTS 1 1 0 2 1 1805 1 1 1 1 }
{PAGENUMBERS 0 1 2 33 1 1 }