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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 257 17 "Campo de dire\347\365es" }}{PARA 256 "" 0 "" {TEXT -1 
3 "por" }}{PARA 256 "" 0 "" {TEXT -1 17 "George Svetlichny" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "restart:with(DEtools):with(plots):
" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 89 "Para tra\347ar um campo de di
re\347\365es \351 preciso utilizar um \"jeitinho\" e expressar uma e.d
.o. " }{TEXT 258 10 "y'=f(t,y) " }{TEXT -1 33 "como o sistema para dua
s fun\347\365es " }{TEXT 259 4 "y(t)" }{TEXT -1 3 " e " }{TEXT 260 4 "
s(t)" }{TEXT -1 6 "  com " }{TEXT 261 18 "dy/dt=f(s(t),y(t))" }{TEXT 
-1 3 " e " }{TEXT 262 7 "ds/dt=1" }{TEXT -1 55 ".  Na defini\347\343o \+
de expr em baixo \351 preciso so escrever " }{TEXT 263 12 "f(s(t),y(t)
)" }{TEXT -1 29 ". Come\347amos com o exemplo de " }{TEXT 264 6 "y'=y+
t" }{TEXT -1 50 ". Vamos plotar o campo num quadrado de tamanho 5. " }
}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 16 "expr:=y(t)+s(t);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 104 "DEplot( \{D(y)(t) = expr, D(s)(t)=1\}, [s(t), y(t)],
\nt=-5..5, s=-5..5, y=-5..5, arrows=line,color='blue');" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 70 "Agora vamos resolver a e.d.o. (se for pos
s\355vel). Primeiro substituimos" }{TEXT 265 3 " t " }{TEXT -1 4 "por \+
" }{TEXT 266 5 "s(t) " }{TEXT -1 8 "em expr." }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 19 "subs(s(t)=t, expr);" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 17 "Formamos a e.d.o." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 14 "eq:=D(y)(t)=%;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 11 "Resolve
mos." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "dsolve(eq,y(t));" }
}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 28 "Impomos uma condi\347\343o incia
l." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "ci:=y(0)=1;" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "dsolve([eq,ci],y(t));" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "subs(%,y(t));" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "plot(%,t=-5..5, y=-5..5);" }}}
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