edos_alto_orden.pdf - Ecuaciones diferenciales ordinarias lineales de alto orden y coeficientes constantes A Coronel Universidad del B\u00edo-B\u00edo Chile

edos_alto_orden.pdf - Ecuaciones diferenciales ordinarias...

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university-logo-filen Ecuaciones diferenciales ordinarias lineales de alto orden y coeficientes constantes A. Coronel Universidad del Bío-Bío, Chile acoronel (UBB) Septiembre 2016 1 / 4
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university-logo-filen Ecuación homogénea y con coeficientes constantes a n d n y dx n + . . . + a 1 dy dx + a 0 y = 0 a n r n + . . . + a 1 r + a 0 = 0 n raíces reales o complejas 1 Si r k es una raíz real se presentan dos casos I Raices repetidas: Si r k tiene multiplicidad m , entonces la solución se forma con la combinación lineal de e r k x , xe r k x , . . . , x m - 1 e r k x I Raices simples: Si r k tiene multiplicidad 1, entonces se forma con e r k x 2 Si r k = α ± β i son raices complejas, se presentan dos casos I Raices complejas repetidas: Si r k tiene multiplicidad m , entonces la solución se forma con la combinación lineal de e α x ( cos ( β x ) + sin ( β x )) , . . . , x m - 1 e α x ( cos ( β x ) + sin ( β x )) I Raices complejas simples: Si r k tiene multiplicidad 1, entonces se forma con e α x ( cos ( β x ) + sin ( β x )) 3 La solución de la ecuación homgénea haciendo una combinación lineal de todas las
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  • Winter '17
  • mabely
  • Ecuación, Ecuación diferencial ordinaria, Ecuación diferencial, Universidad del Bío-Bío, A. Coronel

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