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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 46 "A equa\347\343o diferencial ordin\341ria mais simples: \+
" }{TEXT 258 7 "y'=f(x)" }{TEXT -1 1 "." }{TEXT 257 0 "" }}{PARA 256 "
" 0 "" {TEXT -1 3 "por" }}{PARA 256 "" 0 "" {TEXT -1 17 "George Svetli
chny" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "restart;with(plots)
;with(DEtools);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 16 "Definimos a ed
o " }{TEXT 259 7 "y'=f(x)" }{TEXT -1 23 " na linguagem do Maple." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "eq:=D(y)(x)=f(x);" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 35 "Definimos a fun\347\343o do lado d
ireito." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "f(x):=x^2-5;" }}
}{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "Resolvemos a edo." }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "dsolve(eq,y(x));" }}}{EXCHG {PARA 
0 "" 0 "" {TEXT -1 28 "Note a constante arbitr\341ria " }{TEXT 260 4 "
_C1 " }{TEXT -1 24 "que aparece na resposta." }}{PARA 0 "" 0 "" {TEXT 
-1 36 "Vamos agora impor condi\347\365es inicias." }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 11 "ci:=y(0)=7;" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 46 "Resolvemos agora a edo com a condi\347\343o inicial." }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "dsolve(\{eq,ci\},y(x));" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "ci:=y(1)=-3;" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "dsolve(\{eq,ci\},y(x));" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 38 "Agora uma condi\347\343o inicial arbitr
\341ria." }}}{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 "" 0 "" {TEXT -1 111 "Note que a imposi\347\343o da co
ndi\347\343o inicial determina a constante _C1 que aparece na primeira
 solu\347\343o apresentada." }}{PARA 0 "" 0 "" {TEXT -1 58 "Agora reso
lvemos a edo com outras fun\347\365es do lado direito." }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "f(x):=x^3*exp(-2*x);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "dsolve(eq,y(x));" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 20 "f(x):=(x^2+1)/(x-1);" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 16 "dsolve(eq,y(x));" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 20 "f(x):=(1+x)/(x^2+1);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 16 "dsolve(eq,y(x));" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 16 "f(x):=exp(-x^2);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 16 "dsolve(eq,y(x));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
29 "Aparece na resposta a fun\347\343o " }{TEXT 261 3 "erf" }{TEXT -1 
16 " conhecido como " }{TEXT 262 14 "fun\347\343o de erro" }{TEXT -1 
65 ", usada na teoria de probabilidade e na estat\355stica. Esta fun
\347\343o " }{TEXT 263 16 "n\343o \351 elementar " }{TEXT 264 0 "" }
{TEXT -1 22 "enquanto o integrando " }{TEXT 265 10 "exp(-x^2) " }
{TEXT -1 41 "o \351. A fun\347\343o de erro  \351 um exempleo de  " }
{TEXT 266 15 "fun\347\343o especial" }{TEXT -1 109 ", ou seja uma n
\343o elementar mas que aparece em v\341rias situa\347\365es concretas
 e portanto merece estudos pr\363prios." }}{PARA 0 "" 0 "" {TEXT -1 0 
"" }}{PARA 0 "" 0 "" {TEXT -1 41 "Agora vamos tentar uma fun\347\343o \+
arbitr\341ria." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "f(x):=h(x
);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "dsolve(eq,y(x));" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 44 "Note que a resposta \351 dada por \+
uma integral " }{TEXT 267 10 "indefinida" }{TEXT -1 1 "." }}}{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 "" 
0 "" {TEXT -1 50 "Note que agora a resposta \351 dada por uma integral
 " }{TEXT 268 8 "definida" }{TEXT -1 8 ", e que " }{TEXT 269 36 "a var
i\341vel de integra\347\343o mudou-se de" }{TEXT -1 1 " " }{TEXT 271 
1 "x" }{TEXT -1 1 " " }{TEXT 270 4 "para" }{TEXT -1 1 " " }{TEXT 272 
1 "u" }{TEXT -1 1 "." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "f(x
):=sin(1/x);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "dsolve(eq,y
(x));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 31 "Aqui aparece a fun\347
\343o especial " }{TEXT 273 2 "Ci" }{TEXT -1 1 "." }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 15 "f(x):=sin(e^x);" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 16 "dsolve(eq,y(x));" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 26 "Uma outra fun\347\343o especial " }{TEXT 274 2 "Si" }{TEXT -1 
1 "." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "f(x):=sin(e^(x^2));
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "dsolve(eq,y(x));" }}}
{EXCHG {PARA 0 "" 0 "" {TEXT -1 212 "Note que agora o Maple n\343o pud
e fazer nada, n\343o h\341 no elenco de fun\347\365es epeciais do Mapl
e uma que resolva a edo dada.  A reposta tinha que ser apresentada com
 a integral indicado. Isto n\343o \351 falha do Maple pois: " }{TEXT 
275 73 "em geral, uma equa\347\343o diferencial N\303O pode ser resolv
ida explicitamente. " }{TEXT -1 0 "" }{TEXT 276 86 "Praticamente todos
 os problemas pr\341ticos s\363 podem ser abordados por m\351todos num
\351ricos." }}}}{MARK "0 0 1" 3 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }
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