Certamen 1 - Matemáticas III (2010-3).pdf - Universidad T´ ecnica Federico Santa Mar´ıa Departamento de Matem´atica Casa Central Primer Certamen

Certamen 1 - Matemáticas III (2010-3).pdf - Universidad...

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Universidad T´ ecnica Federico Santa Mar´ ıa Departamento de Matem´ atica Casa Central Primer Certamen Matem´ atica III (MAT023) Jueves 6 de Enero de 2011 Nombre y Apellido del alumno: Rol: ———————————————— ———————– Duraci´ on: 120 minutos. 1. Resolver la ecuaci´on diferencial dy dx = 1 - 3 x - 3 y 1 + x + y 1
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Universidad T´ ecnica Federico Santa Mar´ ıa Departamento de Matem´ atica Casa Central 2. Resolver la ecuaci´on diferencial D ( D - 1)( D 2 + 1) ( y ) = 15 sen (2 x ) 2
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Universidad T´ ecnica Federico Santa Mar´ ıa Departamento de Matem´ atica Casa Central 3. Dada la ecuaci´ on diferencial xy 00 - 2 y 0 + x + 2 x y = x 2 (a) Encuentre la soluci´on homogenea si se conoce que una soluci´on es: y 1 ( x ) = xcos ( x ). (b) Encuentre la soluci´on particular. (c) Encuentre la soluci´on con las c.i.: y π 2 = 2 π ; y 0 π 2 = 2. 3
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Universidad T´ ecnica Federico Santa Mar´ ıa Departamento de Matem´ atica Casa Central 4. (a) Encuentre el dominio, recorrido y la gr´afica de la superficie: x 2 + y 2 + ( z - 2 a ) 2 = 4 a 2 . (b) Encuentre el dominio, recorrido y la gr´ afica de la superficie:
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