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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 92 "#This procedure uses
 the numerical method to solve the differential equation in #demo2.mws
. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with(DEtools);" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 46 "# We firist define the initial val
ued problem:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "diffeq:=dif
f(y(x),x)=x+sin(y(x));" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 14 "inits:=y(0)=1;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
55 "# Then we use dsolve, but include the option \"numeric\":" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "sol:=dsolve(\{diffeq, inits
\}, y(x), numeric);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 50 "# The appr
oximation value of the solution at  x=1:" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 7 "sol(1);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 56 "#If yo
u want to have a picture of the solution, then do:" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 40 "with(plots):odeplot(sol,[x,y(x)],-1..1);" }
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK 
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