Sistemas de equa\303\247\303\265es diferenciais e equa\303\247\303\265es de segunda ordem Solu\303\247\303\265es exatas, num\303\251ricas e por s\303\251ries de sistemas e equa\303\247\303\265es de segunda ordem Dada a equa\303\247\303\243o diferencial de segunda ordem y'' = f(x,y,y') com as condi\303\247\303\265es iniciais y(a) = b e y'(a) = c podemos escrever esta equa\303\247\303\243o no MapleV com o comando do operador de segunda ordem D(D(y)) = (D@@2)(y) ou com o comando da derivada repetida diff(y(x),x,x) = diff(y(x), x$2) . A sintaxe do comando \303\251 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 Como no caso de equa\303\247\303\243o de primeira ordem, os v\303\241rios tipos de solu\303\247\303\243o s\303\243o obtidos com o comando dsolve especificando-se o tipo com type = que pode ser ( exact (defaut), numeric , series ) . 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYsLUkjbWlHRiQ2JVEkU29sRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEqJmNvbG9uZXE7RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtRjY2LVEifkYnRjlGO0Y+RkBGQkZERkZGSC9GS1EmMC4wZW1GJy9GTkZTLUYsNiVRInlGJ0YvRjItSShtZmVuY2VkR0YkNiQtRiM2JS1GLDYlUSJ4RidGL0YyLyUrZXhlY3V0YWJsZUdGPUY5RjktRjY2LVEiPUYnRjlGO0Y+RkBGQkZERkZGSEZKRk0tRiw2JVEiRkYnRi9GMi1GWTYkLUYjNilGZ24tRjY2LVEiLEYnRjlGOy9GP0YxRkBGQkZERkZGSEZSL0ZOUSwwLjMzMzMzMzNlbUYnLUYsNiVRJF9DMUYnRi9GMkZmby1GLDYlUSRfQzJGJ0YvRjJGam5GOUY5RmpuRjk= 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 Dado um sistema de primeira ordem x'=f(x,y,t), y'=g(x,y,t) nas vari\303\241veis dependente (x(t),y(t)), com as condi\303\247\303\265es iniciais (opcionais) x(a) = b e y(a) = c podemos escrever o sistema na forma 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 Resolvemos este sistema com desolve do seguinte modo Lista := dsolve(Sistema, {x(t),y(t)}, type= op\303\247\303\243o, OutrasOp\303\247\303\265es = ...) O retorno \303\251 uma lista com duas igualdades que podem depender de duas constantes 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 Obsevamos que, no caso de um sistema linear, o comando output = basis n\303\243o funciona do mesmo modo que para equa\303\247\303\265es de segunda ordem Exemplo 1: Vamos resolver a equa\303\247\303\243o do oscilador harm\303\264nico y'' + y = 0 sem condi\303\247\303\265es iniciais LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLUkjbWlHRiQ2JVEocmVzdGFydEYnLyUnaXRhbGljR1EldHJ1ZUYnL0YwUSdpdGFsaWNGJy1GLDYtUSI7RidGL0YyL0Y2RkxGN0Y5RjtGPUY/RkEvRkVRLDAuMjc3Nzc3OGVtRicvJStleGVjdXRhYmxlR0Y0Ri8= Oscilador_Harm := (D@@2)(y)(x)+(omega^2) * y(x); a equa\303\247\303\243o ficar\303\241 =0 por default dsolve(Oscilador_Harm, y(x)); d\303\241 a solu\303\247ao geral 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzY/LUkjbWlHRiQ2JVEkU29sRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEifkYnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZMLUY2Ni1RKiZjb2xvbmVxO0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EsMC4yNzc3Nzc4ZW1GJy9GTkZTRjUtRiw2JVEnZHNvbHZlRidGL0YyLUkobWZlbmNlZEdGJDYkLUYjNi4tRiw2JVEvT3NjaWxhZG9yX0ZvcmNGJ0YvRjItRjY2LVEiLEYnRjlGOy9GP0YxRkBGQkZERkZGSEZKL0ZOUSwwLjMzMzMzMzNlbUYnRjUtRiw2JVEieUYnRi9GMi1GWTYkLUYjNiUtRiw2JVEieEYnRi9GMi8lK2V4ZWN1dGFibGVHRj1GOUY5RmpuRjUtRiw2JVEnb3V0cHV0RidGL0YyLUY2Ni1RIj1GJ0Y5RjtGPkZARkJGREZGRkhGUkZULUYsNiVRJmJhc2lzRidGL0YyRmpvRjlGOS1GNjYtUSI7RidGOUY7Rl1vRkBGQkZERkZGSEZKRlRGNS1GLDYlUShkJiMyMjU7RidGL0YyRjUtRiw2JVEkdW1hRidGL0YyRjUtRiw2JVElYmFzZUYnRi9GMkY1LUYsNiVRI2RhRidGL0YyRjUtRiw2JVEyZXF1YSYjMjMxOyYjMjI3O29GJ0YvRjJGNS1GLDYlUS9ob21vZyYjMjM0O25lYUYnRi9GMkY1LUYsNiVRJW1haXNGJ0YvRjJGNUZbcUY1LUYsNiVRMnNvbHUmIzIzMTsmIzIyNztvRidGL0YyRjUtRiw2JVErcGFydGljdWxhckYnRi9GMkZqb0Y5 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 Exemplo 2 : Considere o sistema de equa\303\247\303\265es diferenciais lineares x' = x+y , y'=y . A seguir vamos a) calcular a solu\303\247\303\243o geral deste sistema b) achar uma base de solu\303\247\303\265es para este sistema, c) resolver este sistema por s\303\251ries d) calcular uma solu\303\247\303\243o numerica 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 Ao resolver o sistema na forma geral, o Maple n\303\243o fornece uma base de solu\303\247\303\265es como nas equa\303\247\303\265es de segunda ordem. Podemos dar esta base claculando-se duas solu\303\247\303\265es particualres com condi\303\247\303\265es iniciais x(0)=1, y(0)=0 e x(0)=0, y(0)=1 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 A seguir calculamos as solu\303\247\303\265es de Sist3 por s\303\251ries e uma solu\303\247\303\243o num\303\251rica : 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 Lista5(1); retorna o valor num\303\251rico no ponto t=1 , x(1)=e, y(1)=e Lista5(2); Na sec\303\247\303\243o sobre solu\303\247\303\265es num\303\251ricas de equa\303\247\303\265es de primeira ordem encontramos outros m\303\251todos e tamb\303\251m o modo de plotar as solu\303\247\303\265es num\303\251ricas Exemplo 4. A equa\303\247\303\243o de Bessel de ordem 1 \303\251 dada por y'' +x y' + ( - 1)y =0 . Vamos resolver esta equa\303\247\303\243o com a condi\303\247\303\243o inicial y(0)=1 , y'(0)=0 ,de forma exata, por s\303\251ries e numericamente 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 a solu\303\247\303\243o exata aparece em termos das fun\303\247\303\265es de Bessel da biblioteca do Maple 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 LLis(1.3); avalia a solu\303\247\303\243o num\303\251rica no ponto x=1.3