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{SECT 0 {EXCHG {PARA 205 "" 0 "" {TEXT 206 0 "" }}{PARA 205 "" 0 "" 
{TEXT 206 29 "Some Problems of Section 1.1 " }{TEXT 206 0 "" }}{PARA 
206 "" 0 "" {TEXT 207 0 "" }}{PARA 206 "" 0 "" {TEXT 207 65 "First nee
d to load library of routines where DEplot is contained." }{TEXT 207 
0 "" }}{PARA 206 "" 0 "" {TEXT 207 0 "" }}}{EXCHG {PARA 207 "> " 0 "" 
{MPLTEXT 1 208 8 "restart;" }{MPLTEXT 1 208 0 "" }}}{EXCHG {PARA 207 "
> " 0 "" {MPLTEXT 1 208 14 "with(DEtools):" }{MPLTEXT 1 208 0 "" }}}
{EXCHG {PARA 206 "" 0 "" {TEXT 207 0 "" }}{PARA 208 "" 0 "" {TEXT 209 
40 "Problem 28 Nonautonomous first order ODE" }{TEXT 209 0 "" }}{PARA 
206 "" 0 "" {TEXT 207 0 "" }}{PARA 206 "" 0 "" {TEXT 207 20 "Define th
e equation " }{TEXT 207 0 "" }}{PARA 206 "" 0 "" {TEXT 207 0 "" }}}
{EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 208 31 "eq1:=diff(v(t),t)=exp(-t
)+v(t);" }{MPLTEXT 1 208 0 "" }}}{EXCHG {PARA 206 "" 0 "" {TEXT 207 0 
"" }}{PARA 206 "" 0 "" {TEXT 207 44 "Obtain the direction field for th
is equation" }{TEXT 207 0 "" }}{PARA 206 "" 0 "" {TEXT 207 0 "" }}}
{EXCHG {PARA 207 "> " 0 "" {MPLTEXT 1 208 113 "DEplot(eq1, v(t),t=0..5
,v=-1.2..1,\{[0,-0.7],[0,-0.6],[0,-0.5],[0,-0.55],[0,-0.4]\}, arrows=T
HIN,title=`Figure 1`);" }{MPLTEXT 1 208 0 "" }}}{EXCHG {PARA 207 "> " 
0 "" {MPLTEXT 1 208 121 "DEplot(eq1, v(t),t=0..50,v=-1.2..0.5,\{[0,-0.
5],[0,-0.500001]\},stepsize=0.1,dirgrid=[30,30],arrows=THIN,title=`Fig
ure 1`);" }{MPLTEXT 1 208 0 "" }}}{EXCHG {PARA 206 "" 0 "" {TEXT 207 
0 "" }}}{EXCHG {PARA 206 "" 0 "" {TEXT 207 37 "What can you conclude f
rom the graph?" }{TEXT 207 0 "" }}{PARA 206 "" 0 "" {TEXT 207 171 "The
re is a critical point on the y-axis. Any solution starting above this
 point will grow to infinity and any solution starting below this poin
t will decrease to infinity." }{TEXT 207 0 "" }}{PARA 206 "" 0 "" 
{TEXT 207 61 "Could you identify where this critical value v(0) is loc
ated?" }{TEXT 207 0 "" }}{PARA 206 "" 0 "" {TEXT 207 0 "" }}}{EXCHG 
{PARA 209 "" 0 "" {TEXT 200 0 "" }}{PARA 209 "" 0 "" {TEXT 200 22 "Pro
blem 31 Section 1.1" }{TEXT 200 0 "" }}{PARA 209 "" 0 "" {TEXT 200 0 "
" }}}{EXCHG {PARA 210 "> " 0 "" {MPLTEXT 1 0 32 "eq2:= diff(v(t),t)=2*
t-1-v(t)^2;" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 207 "> " 0 "" 
{MPLTEXT 1 208 87 "DEplot(eq2, v(t),t=0..3,v=-3..3,\{[0,49]\},arrows=T
HIN,dirgrid=[30,30],title=`Figure 1`);" }{MPLTEXT 1 208 0 "" }}}
{EXCHG {PARA 210 "> " 0 "" {MPLTEXT 1 0 138 "DEplot(eq2, v(t),t=0..2,v
=-4..4,\{[0,49]\},arrows=THIN,dirgrid=[30,30],\{[0,1],[0,-1],[0,-0.3],
[0,-.5],[0,4]\},stepsize=0.1,title=`Figure 1`);" }{MPLTEXT 1 0 0 "" }}
}{EXCHG {PARA 210 "> " 0 "" {MPLTEXT 1 0 125 "DEplot(eq2, v(t),t=0..4,
v=-10..10,\{[0,49]\},arrows=THIN,dirgrid=[30,30],\{[0,-0.424],[0,-.422
]\},stepsize=0.1,title=`Figure 1`);" }{MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 210 "> " 0 "" {MPLTEXT 1 0 17 "dsolve(eq2,v(t));" }{MPLTEXT 1 0 
0 "" }}}{EXCHG {PARA 210 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 211 "" 0
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