{VERSION 3 0 "SUN SPARC SOLARIS" "3.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 
0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }}
{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with(DEtools);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 162 "DEplot(D(y)(x)=sin(x)*sin(y
(x)),y(x),x=-Pi..Pi, [[y(0)=0.5],[y(0)=2],[y(0)=-2],[y(0)=-0.5]],\ntit
le=`Problem 1 or 2`,colour=grey,linecolor=[red,green,\nblue,cyan]);" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "de23:=diff(y(x),x)=2*y(x)-
2*y(x)*x;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "s23:=rhs(dsolv
e(\{de23,y(0)=3\},y(x)));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
25 "plot(s23,x=0..2,y=0..10);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 14 "subs(x=1,s23);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "d31
:=x*diff(y(x),x)+2*y(x)=x^(-3);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 17 "dsolve(d31,y(x));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
46 "i45:=\{diff(P(t),t)=P(t)*(1-ln(P(t))), P(0)=1\};" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 27 "s45:=rhs(dsolve(i45,P(t)));" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "simplify(s45,exp);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "subs(exp(Pi*I)=-1,%);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "plot(%,t=0..6);" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 15 "#Problem 5 or 6" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 40 "restart: d56:=m*diff(v(t),t)=m*g-k*v(t);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "m:=250; g:=981/100; k:=25;" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "s56:=rhs(dsolve(\{d56,v(0
)=0\},v(t)));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "x56:=int(s
56,t);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "fsolve(x56-981=50
0,t);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 71 "i64:=\{(1/x+2*x*y(x)^2)+(2*x^2*y(x)-cos(y(x)))*dif
f(y(x),x)=0, y(1)=Pi\};" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "
dsolve(i64,y(x));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 70 "Weird!  \nAn
 exact equation Maple can't solve.  So, give her some help." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "f1:=int(1/x+2*x*y^2,x);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "f1y:=diff(f1,y);" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 53 "This leaves out the constant of integrati
on function:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "dsolve(f1y+
diff(h(y),y)=-cos(y)+2*x^2*y,h(y));" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 16 "solc:=f1+rhs(%);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 34 "solve(subs(\{x=1,y=Pi\}, solc),_C1);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "s64:=subs(_C1=%,solc);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "28 0 0" 22 }{VIEWOPTS 
1 1 0 1 1 1803 }