Question: 2. (5 marks) Let f : R - R be a twice differentiable function such that f+ f =0. Prove there exist constants c and

2. (5 marks) Let f : R - R be a

2. (5 marks) Let f : R - R be a twice differentiable function such that f"+ f =0. Prove there exist constants c and c2 such that, for all real x, f(x) = ci sinx + c2 cosx. We are assuming here that we know all the basic properties of sines and cosines, such as (sinx)' = cosx. (Hint: what can you say about the functions f(x)cosx - f (x) sinx and f(x) sinx+ f'(x) cosx?)

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