**Unformatted text preview: **t and y 00 p =-16 A cos 4 t-16 B sin 4 t . Crunching everything through, we get (-16 A cos 4 t-16 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 A-8 B ) cos 4 t + (-15 B + 8 A ) sin 4 t = sin 4 t Hence we must solve the simultaneous equations-15 A-8 B = 0 and-15 B + 8 A = 1. From the ﬁrst 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 t-15 289 sin 4 t. s 1...

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- Spring '07
- staff
- Math, Sin