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Unformatted text preview: t and y 00 p =16 A cos 4 t16 B sin 4 t . Crunching everything through, we get (16 A cos 4 t16 B sin 4 t ) + (8 B cos 4 t + 8 A sin 4 t ) + ( A cos 4 t + B sin 4 t ) = sin 4 t (15 A8 B ) cos 4 t + (15 B + 8 A ) sin 4 t = sin 4 t Hence we must solve the simultaneous equations15 A8 B = 0 and15 B + 8 A = 1. From the rst equation, we get B =15 8 A . Plugging this into the second, we have 225 8 A + 8 A = 1, or 289 8 A = 1. Hence A = 8 289 . Since B =15 8 A , we have B =15 289 . Putting everything together, we get y = C 1 e t + C 2 te t + 8 289 cos 4 t15 289 sin 4 t. s 1...
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 Spring '07
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 Math

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