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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 35 "Jonathan Terrell and Antho
ny Parker" }}{PARA 0 "" 0 "" {TEXT -1 17 "February 14, 2000" }}{PARA 
0 "" 0 "" {TEXT -1 22 "Differential Equations" }}{PARA 0 "" 0 "" 
{TEXT -1 15 "Maple Project 2" }}{PARA 0 "" 0 "" {TEXT -1 16 "Problem S
et B #2" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 35 "Consider the initial v
alue problem:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 23 "xy' + y = 2x,  y(1) = c" }}{PARA 0 "" 0 "" {TEXT -1 0 "" 
}}{PARA 0 "" 0 "" {TEXT -1 20 "Solve it using Maple" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 42 "DE := \{x*diff(y(x),x)+y(x)=2*x, y(1) = c\};" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#DEG<$/,&*&%\"xG\"\"\"-%%diffG6$-%\"
yG6#F)F)F*F*F.F*,$F)\"\"#/-F/6#F*%\"cG" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 24 "sol := dsolve(DE, y(x));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%$solG/-%\"yG6#%\"xG,&F)\"\"\"*&,&!\"\"F+%\"cGF+\"\"\"
F)!\"\"F+" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 27 "f is a function of f
 and c." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "f := unapply(sim
plify(rhs(sol)),x,c);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGR6$%\"x
G%\"cG6\"6$%)operatorG%&arrowGF)*&,(*$)9$\"\"#\"\"\"\"\"\"!\"\"F49%F4F
3F1!\"\"F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 91 "Use Maple to graph the solutions f
or c = 0.8, 0.9, 1, 1.1, 1.2 on the interval (0.75,1.25)." }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 22 "Syntax is from demo 2." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 40 "plot(\{f(x,c*0.1) $c=8..12\},x=.75..1.25);" }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 13 "" 1 "" {GLPLOT2D 220 180 
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1.000000 45.000000 45.000000 0 }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 48 
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> " 0 "" {MPLTEXT 1 0 26 "f(0.01,c*0.1) $ c = 8..12;" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6'$!%**>!\"#$!$***F%$\"\"\"F%$\"%,5F%$\"%,?F%" }}}
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{TEXT -1 65 "Plot all of the five solutions together on the interval (
0,0.25)." }}{PARA 0 "" 0 "" {TEXT -1 74 "How does changes in the initi
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{TEXT -1 29 "or x-> 0 from the right side?" }}}{EXCHG {PARA 0 "> " 0 "
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