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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT 256 19 "ENGI 3424 Chapter 2" }
{TEXT -1 51 " - Demonstration of Maple for the solution of some " }}
{PARA 0 "" 0 "" {TEXT -1 79 "second order linear ordinary differential
 equations with constant coefficients," }}{PARA 0 "" 0 "" {TEXT -1 39 
"using examples from the lecture notes.." }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 14 "with(DEtools):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
13 "Example 2.2.1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "ode :=
 diff(y(x),x,x) + 2*diff(y(x),x) - 3*y(x) = x^2 + exp(2*x);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%$odeG/,(-%%diffG6$-%\"yG6#%\"xG-%\"$G6$F-
\"\"#\"\"\"*&F1F2-F(6$F*F-F2F2*&\"\"$F2F*F2!\"\",&*$)F-F1F2F2-%$expG6#
,$*&F1F2F-F2F2F2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "dsolve(
ode, y(x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"yG6#%\"xG,.*&-%$ex
pGF&\"\"\"%$_C2GF,F,*&-F+6#,$*&\"\"$F,F'F,!\"\"F,%$_C1GF,F,*&F3F4F'\"
\"#F4*(\"\"%F,\"\"*F4F'F,F4#\"#9\"#FF4*&#F,\"\"&F,-F+6#,$*&F7F,F'F,F,F
,F," }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 13 "Example 2.2.2" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "ode := diff(y(x),x,x) + y(x) = tan(
x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$odeG/,&-%%diffG6$-%\"yG6#%\"
xG-%\"$G6$F-\"\"#\"\"\"F*F2-%$tanGF," }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 18 "dsolve(ode, y(x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#/-%\"yG6#%\"xG,(*&-%$sinGF&\"\"\"%$_C2GF,F,*&-%$cosGF&F,%$_C1GF,F,*&F
/F,-%#lnG6#*&,&F,F,F*F,F,F/!\"\"F,F8" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 13 "Example 2.2.3" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "ode
 := diff(y(x),x,x) -2*diff(y(x),x) + y(x) = exp(x);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%$odeG/,(-%%diffG6$-%\"yG6#%\"xG-%\"$G6$F-\"\"#\"\"
\"*&F1F2-F(6$F*F-F2!\"\"F*F2-%$expGF," }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 25 "ics := y(0)=0, D(y)(0)=1;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%$icsG6$/-%\"yG6#\"\"!F*/--%\"DG6#F(F)\"\"\"" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "dsolve(\{ode,ics\}, y(x));" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"yG6#%\"xG,&*&-%$expGF&\"\"\"F'F
,F,*&#F,\"\"#F,*&)F'F/F,F*F,F,F," }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
53 "Example 2.2.4 - an ODE with non-constant coefficients" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "ode := x^2*diff(y(x),x,x) -5*x*diff
(y(x),x) + 8*y(x) = 3*x;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$odeG/,(
*&)%\"xG\"\"#\"\"\"-%%diffG6$-%\"yG6#F)-%\"$G6$F)F*F+F+*(\"\"&F+F)F+-F
-6$F/F)F+!\"\"*&\"\")F+F/F+F+,$*&\"\"$F+F)F+F+" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 18 "dsolve(ode, y(x));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#/-%\"yG6#%\"xG,(*&)F'\"\"%\"\"\"%$_C2GF,F,*&)F'\"\"#F,%
$_C1GF,F,F'F," }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 32 "Example 2.4.1 - \+
higher order ODE" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 102 "ode :=
 diff(y(x),x$5) + 2*diff(y(x),x$4) - 3*diff(y(x),x$3) - 4*diff(y(x),x,
x) + 4*diff(y(x),x) = 8*x;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$odeG/
,,-%%diffG6$-%\"yG6#%\"xG-%\"$G6$F-\"\"&\"\"\"*&\"\"#F2-F(6$F*-F/6$F-
\"\"%F2F2*&\"\"$F2-F(6$F*-F/6$F-F;F2!\"\"*&F9F2-F(6$F*-F/6$F-F4F2F@*&F
9F2-F(6$F*F-F2F2,$*&\"\")F2F-F2F2" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 18 "dsolve(ode, y(x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#/-%\"yG6#%\"xG,0*$)F'\"\"#\"\"\"F,*&%$_C1GF,-%$expGF&F,F,*&#F,F+F,*&%
$_C2GF,-F06#,$*&F+F,F'F,!\"\"F,F,F9*&%$_C3GF,,&*&F/F,F'F,F,F/F9F,F,*&%
$_C4GF,,&*&#F,F+F,*&F5F,F'F,F,F9*&#F,\"\"%F,F5F,F9F,F,*&F+F,F'F,F,%$_C
5GF," }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 32 "Example 2.4.2 - higher or
der ODE" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "ode := EI*diff(y
(x),x$4) = W;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$odeG/*&%#EIG\"\"\"
-%%diffG6$-%\"yG6#%\"xG-%\"$G6$F/\"\"%F(%\"WG" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 56 "ics := y(0)=0, D(y)(0)=0, D(D(y))(L)=0, D(D(D(y)
))(L)=0;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$icsG6&/-%\"yG6#\"\"!F*/
--%\"DG6#F(F)F*/---%#@@G6$F.\"\"#F/6#%\"LGF*/---F46$F.\"\"$F/F7F*" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "dsolve(\{ode,ics\}, y(x));" 
}}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"yG6#%\"xG,(**\"#C!\"\"%\"WG\"\"
\"%#EIGF+F'\"\"%F-*,\"\"'F+F,F-F.F+%\"LGF-F'\"\"$F+*,F/F+F,F-F.F+F2\"
\"#F'F5F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "0 \+
2 0" 38 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }