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{SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT -1 0 "" }{TEXT 256 48 "MAT1154 \+
- Equa\347\365es Diferenciais e de Diferen\347as " }}{PARA 257 "" 0 "
" {TEXT -1 55 "Uma equa\347\343o diferencial ordin\341ria n\343o na fo
rma normal.." }{TEXT 257 0 "" }}{PARA 256 "" 0 "" {TEXT -1 3 "por" }}
{PARA 256 "" 0 "" {TEXT -1 17 "George Svetlichny" }}}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "restart;with
(DEtools);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 19 "Considere a equ\347
\343o " }{TEXT 259 19 "(y')**2 -xy'+x**2=0" }{TEXT -1 1 "." }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "eq:=D(y)(x)**2-x*D(y)(x)-2*x**2=0;
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 22 "Podemos resolver para " }
{TEXT 260 3 "y' " }{TEXT -1 29 "para achar as formas normais." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "solve(eq, D(y)(x));" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 81 "Potanto a equa\347\343o original s
e desdobra em duas equa\347\365es em forma normal, a saber " }{TEXT 
261 7 "y' = -x" }{TEXT -1 4 ", e " }{TEXT 262 7 "y' = 2x" }{TEXT -1 
54 ". Vamos agora resolver a equa\347\343o diferencial original." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "dsolve(eq, y(x));" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 63 "Note que h\341 duas solu\347\365es
, corespondendo \340s duas solu\347\365es para " }{TEXT 263 2 "y'" }
{TEXT -1 66 " que encontramos acima. Note a presen\347a de constantes \+
arbitr\341rios." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 35 "Impomos agora uma condi\347\343o inicial." }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "ci:=y(1)=-3;" }}}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 61 "E resolvemos a equa\347\343o diferencial com esta co
ndi\347\343o inicial." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "ds
olve([eq,ci],y(x));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 101 "Note que \+
a condi\347\343o inicial determinou o valor da constante arbitr\341ria
 em cada uma das duas solu\347\365es." }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 0 "" 0 "" {TEXT -1 81 "Vamos agor inpor uma condi\347\343o i
nicial generica e resolver a equa\347\343o diferencial.." }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "ci:=y(a)=b;" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 21 "dsolve([eq,ci],y(x));" }}}{EXCHG {PARA 0 "> " 
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