Question: Solve the initial value problem x + 64x = 3 cos(6t), x(0) = 2, x'(0) = 1 (where primes indicate derivatives with respect to t).

Solve the initial value problem x" + 64x = 3 cos(6t), x(0) = 2, x'(0) = 1 (where primes indicate derivatives with respect to t). Express your solution as the sum of two oscillations, x(t) = cos cos t ) (Ensure that the phase shift in your answer is a number between 0 and 2It.)

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