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{SECT 0 {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 259 "" 0 "" {TEXT 260 
46 "How to Solve Differential Equations with Maple" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 31 "To define a derivative, u
se the" }{TEXT 257 1 " " }{HYPERLNK 17 "diff" 2 "diff" "" }{TEXT 258 
1 " " }{TEXT -1 7 "command" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "ode1 := cos(x)*diff(y(x),x) +sin(x)
*y(x)= 1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%ode1G/,&*&-%$cosG6#%\"
xG\"\"\"-%%diffG6$-%\"yGF*F+F,F,*&-%$sinGF*F,F0F,F,F," }}}{PARA 256 "
" 0 "" {TEXT -1 0 "" }}{PARA 256 "" 1 "" {TEXT -1 26 "To solve an ODE,
 use the  " }{TEXT 256 6 "dsolve" }{TEXT -1 11 "  command:." }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "ds
olve(ode1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"yG6#%\"xG,&*&-%$co
sGF&\"\"\"-%$tanGF&F,F,*&F*F,%$_C1GF,F," }}}{PARA 258 "" 1 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 28 "Define an initial condition:" }
}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 11 "IC:=y(0)=1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#ICG/-%\"yG6#\"
\"!\"\"\"" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 4 "Use " }{TEXT 259 6 "dsolve" }{TEXT -1 18 " to solve an IVP: " }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
19 "dsolve(\{ode1, IC\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"yG6#
%\"xG,&*&-%$cosGF&\"\"\"-%$tanGF&F,F,F*F," }}}{PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 17 "Riccati equation:" }}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "ode2 \+
:= diff(y(x),x)= sin(x)*y(x)+cos(x)*y(x)^2+x;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%%ode2G/-%%diffG6$-%\"yG6#%\"xGF,,(*&-%$sinGF+\"\"\"F)
F1F1*&-%$cosGF+F1)F)\"\"#F1F1F,F1" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 13 "dsolve(ode2);" }}}{EXCHG }{PARA 0 "" 0 "" {TEXT -1 0 
"" }}{PARA 260 "" 0 "" {TEXT 262 23 "Maple can NOT solve it!" }}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 47 "To know how to \+
use these above commands, go to " }{TEXT 261 10 "MAPLE HELP" }}}{MARK 
"28" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }