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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 60 "This section is really sim
ple if you know the Euler formula " }{XPPEDIT 18 0 "exp(I*t)=cos(t)+I*
sin(t);" "/-%$expG6#*&%\"IG\"\"\"%\"tGF(,&-%$cosG6#F)F(*&F'F(-%$sinG6#
F)F(F(" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 139 "Oh, you also n
eed to realize that if a DE has real coefficients then the real and im
aginary parts of a complex solution are real solutions." }}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 8 "4.6  #22" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "d22:=diff(y(x),x,x)+2*diff(y
(x),x)+17*y(x)=0;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "i22:=
\{d22,y(0)=1,D(y)(0)=-1\};" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
17 "dsolve(i22,y(x));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 49 "4.6  #28
  One of yours, but here is a head start." }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 65 "i28:=\{diff(y(x),x,x)+b*diff(y(x),x)+4*y(x)=0, y(0)
=1, D(y)(0)=0\};" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "b:=5:so
l5:=rhs(dsolve(i28,y(x)));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
33 "b:=2:sol2:=rhs(dsolve(i28,y(x)));" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 25 "plot(\{sol2,sol5\},x=0..3);" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 8 "4.6  #29" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 80 "d
29a:=diff(y(x),x,x,x)-diff(y(x),x,x)+diff(y(x),x)+ 3*y(x)=0; dsolve(d2
9a,y(x));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 85 "d29b:=diff(y(x
),x,x,x)+2*diff(y(x),x,x)+ 5*diff(y(x),x)-26*y(x)=0; dsolve(d29b,y(x))
;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "d29c:=diff(y(x),x,x,x,
x)+13*diff(y(x),x,x)+36*y(x)=0; dsolve(d29c,y(x));" }}}{EXCHG {PARA 0 
"" 0 "" {TEXT -1 60 "(The problem in the book contains a typo: they le
ft out the " }{XPPEDIT 18 0 "y" "I\"yG6\"" }{TEXT -1 15 " after the 36
.)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 58 "4.6  #41  Repeated complex \+
roots are no problem for Maple." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 68 "d41a:=diff(y(x),x,x,x,x)+2*diff(y(x),x,x)+y(x)=0;\ndsolve(d41a
,y(x));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 108 "d41b:=diff(y(x)
,x,x,x,x)+4*diff(y(x),x,x,x)+ 12*diff(y(x),x,x)+16*diff(y(x),x)+16*y(x
)=0;\ndsolve(d41b,y(x));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 31 "[They
 did it again (left off a " }{XPPEDIT 18 0 "y" "I\"yG6\"" }{TEXT -1 3 
").]" }}}}{MARK "0 0 0" 14 }{VIEWOPTS 1 1 0 2 1 1805 }