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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "deq:=diff(y(x),x)=y(
x)*cos(x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with(DETools)
:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "DEplot(deq,y(x),x=0..P
i,y=-2.5..2.5);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "DEplot(d
eq,y(x),x=0..Pi,y=-2.5..2.5,[[Pi/2,-2]]);" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 39 "initial_data_point:=[evalf(Pi/2,3),-2];" }}}{EXCHG
{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "dsolve(deq,y(x));" }}}{EXCHG {PARA
0 "> " 0 "" {MPLTEXT 1 0 30 "dsolve(\{deq,y(Pi/2)=-2\},y(x));" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 69 "Rightclick menus on the output ena
ble you to easily evaluate this at " }{XPPEDIT 18 0 "x = 0;" "6#/%\"xG
\"\"!" }{TEXT -1 25 " and then approximate it:" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 41 "y(x) = Eval(-2/exp(1)*exp(sin(x)),x = 0);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "y(x) = value(Eval(-2/exp(1)*
exp(sin(x)),x = 0));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "y(x
) = evalf[5](-2/exp(1));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 88 "The s
ubstitute command seems pretty easy to swallow, followed by the value \+
command, no?:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "subs(y(x) \+
= -2/exp(1)*exp(sin(x)),deq);\nvalue(%);\nlhs(%)-rhs(%);" }}}{EXCHG
{PARA 0 "" 0 "" {TEXT -1 99 "It is a lot easier to see that a differen
ce is zero than to compare two expressions piece by piece." }}}}{MARK
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