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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 19 "ENGI 9420 Chapter 1" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with(DEtools):" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 24 "Example 1.01.1   Speed  " }{XPPEDIT 18 0 
"v(t);" "6#-%\"vG6#%\"tG" }{TEXT -1 41 "  of object falling through vi
scous fluid" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "ode1 := diff
(v(t),t) + b/m*(v(t))^2 - g; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%od
e1G,(-%%diffG6$-%\"vG6#%\"tGF,\"\"\"*(%\"bGF-%\"mG!\"\"F)\"\"#F-%\"gGF
1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "dsolve(ode1);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"vG6#%\"tG*(-%%tanhG6#*(*(%\"gG\"
\"\"%\"bGF/%\"mGF/#F/\"\"#,&F'F/%$_C1GF/F/F1!\"\"F/F-F2F0F6" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "ics1 := v(0) = 0;" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%%ics1G/-%\"vG6#\"\"!F)" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 21 "dsolve(\{ode1, ics1\});" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#/-%\"vG6#%\"tG*(-%%tanhG6#*(F'\"\"\"*(%\"gGF-%\"bGF-%
\"mGF-#F-\"\"#F1!\"\"F-F.F2F0F4" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
14 "Example 1.02.1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "ode1 \+
:= (y(x)*exp(x) - x) + exp(x)*diff(y(x),x);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%%ode1G,(*&-%\"yG6#%\"xG\"\"\"-%$expGF)F+F+F*!\"\"*&F,
F+-%%diffG6$F'F*F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "dso
lve(ode1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"yG6#%\"xG*&,&*&\"\"
#!\"\"F'F+\"\"\"%$_C1GF-F--%$expG6#,$F'F,F-" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 30 "Example 1.03.2 - solution for " }{TEXT 256 1 "y" }
{TEXT -1 18 " as a function of " }{TEXT 257 1 "x" }{TEXT -1 21 " is ve
ry complicated:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "ode1 := \+
2*x*y(x) + (2*x^2 + 3*y(x))*diff(y(x),x);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%%ode1G,&*(\"\"#\"\"\"%\"xGF(-%\"yG6#F)F(F(*&,&*&F'F()
F)F'F(F(*&\"\"$F(F*F(F(F(-%%diffG6$F*F)F(F(" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 13 "dsolve(ode1);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6+/
-%\"yG6#%\"xG*&,(*(\"\"'!\"\"F'!\"#,(*&\"\")\"\"\")F'F+F1F,*&\"$3\"F1)
%$_C1G\"\"#F1F1*(\"#7F1F6F1,&*&F9F1F2F1F,*&\"#\")F1F5F1F1#F1F7F1#F1\"
\"$F1**F7F1F@F,F'F7F.#F,F@F1#F1F@F,F1)F'F7F1/F$*(F)F1),&#F1F7F,*&^#F>F
1F@F>F1F@F1FDF1/F$*(F)F1FDF1),&#F1F7F,*&^##F,F7F1F@F>F1F@F1/F$,$*(\"%G
<F,,**(\"$W\"F1F'F-F.F?F,*(\"$w&F1F'F7F.FBF,FfnF,*(^#\"$k)F1F@F>,&*(F+
F,F'F-F.F?F1**F7F1F@F,F'F7F.FBF,F1F1F1F'F7F1/F$,$*(FWF,,**(FZF1F'F-F.F
?F,*(FfnF1F'F7F.FBF,FfnF,*(^#!$k)F1F@F>FjnF1F1F1F'F7F1/F$,$**FWF,FHF@F
XF1F'F7F1/F$,$**FWF,FOF@FXF1F'F7F1/F$,$**FWF,FHF@F`oF1F'F7F1/F$,$**FWF
,FOF@F`oF1F'F7F1" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "but solution \+
for " }{TEXT 258 1 "x" }{TEXT -1 18 " as a function of " }{TEXT 259 1 
"y" }{TEXT -1 17 " is much simpler:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 51 "ode1 := 2*x(y)*y*diff(x(y),y) + (2*(x(y))^2 + 3*y);" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%ode1G,(**\"\"#\"\"\"-%\"xG6#%\"yG
F(F,F(-%%diffG6$F)F,F(F(*&F'F()F)F'F(F(*&\"\"$F(F,F(F(" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "dsolve(ode1);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6$/-%\"xG6#%\"yG*&,&*$)F'\"\"$\"\"\"!\"\"%$_C1GF-#F-\"\"#
F'F./F$,$F(F." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 14 "Example 1.04.1" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "ode1 := diff(y(x),x) + 2*
y(x)/x = 1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%ode1G/,&-%%diffG6$-%
\"yG6#%\"xGF-\"\"\"*(\"\"#F.F*F.F-!\"\"F.F." }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 13 "dsolve(ode1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/
-%\"yG6#%\"xG,&*&\"\"$!\"\"F'\"\"\"F,*&F'!\"#%$_C1GF,F," }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 70 "Example 1.04.4 simple inductor-resistor c
ircuit with ac voltage supply" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 54 "ode1 := diff(i(t),t) + 400000*i(t) = -500000*sin(5*t);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%%ode1G/,&-%%diffG6$-%\"iG6#%\"tGF-\"\"\"*&
\"'++SF.F*F.F.,$*&\"'++]F.-%$sinG6#,$*&\"\"&F.F-F.F.F.!\"\"" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "ics1 := i(0) = 1;" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%%ics1G/-%\"iG6#\"\"!\"\"\"" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "dsolve(\{ode1, ics1\});" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#/-%\"iG6#%\"tG,(*&#\"'++5\"+,+++k\"\"\"-%$co
sG6#,$*&\"\"&F-F'F-F-F-F-*&#\"+++++!)F,F--%$sinGF0F-!\"\"*&#\"+,+!**R'
F,F--%$expG6#,$*&\"'++SF-F'F-F9F-F-" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 42 "Example 1.05.1   Logistic population model" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 43 "ode1 := diff(y(x),x) = a*y(x) - b*(y(x))^2;
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%ode1G/-%%diffG6$-%\"yG6#%\"xGF,
,&*&%\"aG\"\"\"F)F0F0*&%\"bGF0)F)\"\"#F0!\"\"" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 13 "dsolve(ode1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#/-%\"yG6#%\"xG*&%\"aG\"\"\",&%\"bGF**(-%$expG6#,$*&F)F*F'F*!\"\"F*%$_
C1GF*F)F*F*F3" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}
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