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{SECT 0 {EXCHG {PARA 260 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 260 "" 0 "" {TEXT 256 84 "Math 334 Nonhomogeneou
s Equations; Method of Undetermined Coefficients              " }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 257 33 "Defining
 a second order equation:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
261 "> " 0 "" {MPLTEXT 1 0 65 "ec:= diff(y(t),t$2) -2*diff(y(t),t) - 3
*y(t) = 5*exp(2*t)*sin(t);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT 258 51 "Finding the general solution for the abo
ve equation" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 261 "> " 0 "" 
{MPLTEXT 1 0 16 "dsolve(ec,y(t));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }
}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 259 0 "" }{TEXT 260 42 "Another \+
example of a second order equation" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "ec2:= diff(y(t),t$2) -2*dif
f(y(t),t) - 3*y(t) = 6*exp(4*t);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 17 "dsolve(ec2,y(t));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT 261 16 "Another example " }}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "ec3:
= diff(y(t),t$2) -2*diff(y(t),t) - 3*y(t) = 3*cos(6*t);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "dsolve(ec3,y(t));" }}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 260 "
" 0 "" {TEXT -1 31 "Simplify the exponential terms." }}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "combine(d
solve(ec3,y(t)),exp);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 262 14 "More exa
mples:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 56 "ec4:= diff(y(t),t$2) -2*diff(y(t),t) - 3*y(t) = 2*t^2
+3;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "dsolve(ec4,y(t));" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "ec5:= diff(y(t),t$2) -2*di
ff(y(t),t) - 3*y(t) = 4*exp(3*t);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 17 "dsolve(ec5,y(t));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT 263 11 "A long one:" }}{PARA 0 "" 0 "
" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 96 "ec6:= dif
f(y(t),t$2) -2*diff(y(t),t) - 3*y(t) = 6*exp(4*t)+3*cos(6*t)+2*t^2+3+5
*exp(2*t)*sin(t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "dsolve
(ec6,y(t));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "combine(dsol
ve(ec6,y(t)),exp);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 
"" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 73 "ec7:= diff(y(t),t$2) -10*diff(y(t),t) + 2
5*y(t) = 10*exp(5*t) + cos(5*t);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 17 "dsolve(ec7,y(t));" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 264 64 "Solving an initia
l value problem. Pay attention to the sintaxis." }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "ec8:= diff(
y(t),t$2) +2*diff(y(t),t) + 5*y(t) = 4*exp(-t)*cos(2*t);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "dsolve(\{ec8,y(0)=1,D(y)(0)=0\}, y(
t));" }}}{EXCHG {PARA 262 "" 0 "" {TEXT 265 23 "Higher order equations
:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 262 "" 0 "" {TEXT -1 23 "Pr
oblem 11 Sectrion 4.3" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "ec9:= diff(y(t),t$3)-3*diff(y(t),t$
2) +2*diff(y(t),t) = t+ exp(t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 17 "dsolve(ec9,y(t));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
31 "simplify(dsolve(ec9,y(t)),exp);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT 266 16 "Solving the IVP:" }}{PARA 0 "
" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "dsol
ve(\{ec9,y(0)=1,D(y)(0)=-1/4,(D@@2)(y)(0)=-3/2\},y(t));" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "y9:= unapply(rhs(dsolve(\{ec9,y(0)=
1,D(y)(0)=-1/4,(D@@2)(y)(0)=-3/2\},y(t))),t);" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 20 "plot(y9(t), t=0..1);" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 21 "plot(y9(t), t=0..10);" }}}{EXCHG {PARA 0 "> " 0 "" 
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