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**Unformatted text preview: **2 3 D + 10 ) [ y p ( x )] = (34 x 16) e 2 x 10 x 2 + 6 x + 34 (34 C x + 17 C 1 16 C ) e 2 x + 10 C 2 x 2 + (10 C 3 6 C 2 ) x +10 C 4 3 C 3 4 C 2 = (34 x 16) e 2 x 10 x 2 + 6 x + 34 . Equating corresponding coecients, we obtain the system 34 C = 34 , 17 C 1 16 C = 16 , 10 C 2 = 10 , 10 C 3 6 C 2 = 6 , 10 C 4 3 C 3 4 C 2 = 34 C = 1 , C 1 = 0 , C 2 = 1 , C 3 = 0 , C 4 = 3 . Thus, y p ( x ) = x 2 e 2 x x 2 + 3 and y ( x ) = y h ( x ) + y p ( x ) = c 1 e 2 x + ( c 2 cos x + c 3 sin x ) e 2 x + x 2 e 2 x x 2 + 3 371...

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