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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 15 "MATH 308 Honors" }}{PARA 0 "" 0 "" {TEXT 
-1 11 "Section 200" }}{PARA 0 "" 0 "" {TEXT -1 11 "Spring 2000" }}
{PARA 0 "" 0 "" {TEXT -1 10 "P. Yasskin" }}{PARA 0 "" 0 "" {TEXT -1 0 
"" }}{PARA 0 "" 0 "" {TEXT -1 12 "Exam 1 Maple" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "with(plots)
:with(DEtools):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "#7" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "deq:=diff(y(t),t)=exp(t)-y(t);" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "#7a" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 17 "dsolve(deq,y(t));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 3 "#7b" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "init:=y(0)=4;
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "dsolve(\{deq,init\},y(t
));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 5 "#7c,d" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 83 "DEplot(deq,y(t), t=-4..6, [[0,-4],[0,-2],[0,0
],[0,2],[0,4],[0,6]], y(t)=-100..100);" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 3 "#7e" }}{PARA 0 "" 0 "" {TEXT -1 40 "Asymptotically, the so
lution looks like " }{MPLTEXT 0 21 15 "y(t) = exp(t)/2" }{TEXT -1 29 "
 .  This begins at about t=3." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "#
8" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "deq:=diff(y(x),x)=cos(
x)+sin(y(x));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "init:=y(0)
=1;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "#8a" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 24 "dsolve(\{deq,init\},y(x));" }}}{EXCHG {PARA 0 
"" 0 "" {TEXT -1 47 "Maple does nothing.  It cannot find a solution." 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "F:=(x,y)->cos(x)+sin(y);
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "y0:=1;" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 11 "y1:=F(0,1);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "F1:=dif
f(F(x,y(x)),x):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "F1:=subs
(diff(y(x),x)=F(x,y),y(x)=y,F1):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 20 "F1:=unapply(F1,x,y);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 12 "y2:=F1(0,1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "F2:=diff(F1(x,y(x)
),x):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "F2:=subs(diff(y(x)
,x)=F(x,y),y(x)=y,F2):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "F
2:=unapply(F2,x,y);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "y3:=
F2(0,1);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "F3:=diff(F2(x,y(x)),x):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "F3:=subs(diff(y(x),x)=F(x,y),y(x)=y
,F3):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "F3:=unapply(F3,x,y
);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "y4:=F3(0,1);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 51 "ftaylor:=y0+y1*x+1/2*y2*x^2+1/6*y3*x^3+1/24*y4*x^4;
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalf(%);" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 3 "#8b" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 54 "dplot:=DEplot(deq,y(x), x=-4..4, [[0,1]], y(x)=-2..6):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "tplot:=plot(ftaylor,x=-4..4,
y=-2..6, color=blue, thickness=3):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 21 "display(dplot,tplot);" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 76 "The taylor ploynomial is a good approximation on about th
e interval [-1,1].." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1 ";" }}
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