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{SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
-1 54 "Maple Worksheet:  Problems 15, 16, 23, 24, Section 5.2" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 43 "DE15:=diff(y(x),x$2)-x*diff(y(x),x)-y(x)=0;" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 9 "Order:=5;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 50 "Y1:=dsolve(\{DE15,y(0)=2,D(y)(0)=1\},y(x),'series');
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "Yp15_4:=convert(rhs(Y1)
,polynom);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "Order:=6;" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "Y2:=dsolve(\{DE15,y(0)=2,D(y
)(0)=1\},y(x),'series');" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 
"Yp15_5:=convert(rhs(Y2),polynom);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 30 "plot(\{Yp15_4,Yp15_5\},x=-2..2);" }}}{EXCHG {PARA 0 "
" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 11 "Problem 16:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "DE16:=(2+x^2)*diff(y(x),x$2)
-x*diff(y(x),x)+4*y(x)=0;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 
"Order:=5;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "Y1:=dsolve(\{
DE16,y(0)=-1,D(y)(0)=3\},y(x),'series');" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 33 "Yp15_4:=convert(rhs(Y1),polynom);" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 9 "Order:=6;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 51 "Y2:=dsolve(\{DE16,y(0)=-1,D(y)(0)=3\},y(x),'series');
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "Yp15_5:=convert(rhs(Y2)
,polynom);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "plot(\{Yp15_4
,Yp15_5\},x=-2..2);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT -1 86 "Problems 23 and 24 ask us to expand the interva
l and look at more terms of the series." }}{PARA 0 "" 0 "" {TEXT -1 0 
"" }}{PARA 0 "" 0 "" {TEXT -1 73 "The solution for problem 23 is not q
uite as nice as the ones in the text:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 21 "for j from 1 to 10 do" }}{PARA 0 "> " 0 "" {MPLTEXT 
1 0 13 "    Order:=j:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "    Y:=dso
lve(\{DE15,y(0)=1,D(y)(0)=0\},y(x),'series'):" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 35 "    Yp[j]:=convert(rhs(Y),polynom):" }}{PARA 0 "> " 
0 "" {MPLTEXT 1 0 7 "end do:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 27 "Yout:=[seq(Yp[j],j=1..10)];" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 27 "plot(Yout,x=-3..3,y=0..10);" }}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 20 "Same for Problem 24:" }
}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 21 "for j from 1 to 20 do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "    \+
Order:=j:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "    Y:=dsolve(\{DE16,y
(0)=1,D(y)(0)=0\},y(x),'series'):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
35 "    Yp[j]:=convert(rhs(Y),polynom):" }}{PARA 0 "> " 0 "" {MPLTEXT 
1 0 7 "end do:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "Yout:=[se
q(Yp[j],j=1..10)];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "plot(
Yout,x=-3..3,y=-10..10,color=black);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 79 "Just for fun, let's look at the
 example from the text and reproduce the figure:" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "DE:=diff(y(
x),x$2)-x*y(x)=0;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "for j \+
from 1 to 16 do" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "    Order:=3*j+1
:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "    Y:=dsolve(\{DE,y(0)=1,D(y)
(0)=0\},y(x),'series'):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "    Yp[j
]:=convert(rhs(Y),polynom):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "end d
o:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "Yout:=[seq(Yp[j],j=1.
.10)];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "plot(Yout,x=-8..2
,y=-2..2,color=black,numpoints=100);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}
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