# Is there an option to let DSolve output exponential functions in preference to trigonometric functions as default results?

For example,

DSolve[y''[x] + y[x] == 0, y[x], x]


gives

{{y[x] -> C[1] Cos[x] + C[2] Sin[x]}}


as the result.

Can we add any option(s) to make us get

{{y[x] -> C[1] E^(I x) + C[2] E^(-I x)}}


Maybe TrigToExp would be suggested, but it will lead to extra 1/2 factor in the solutions.
Update1: Admittedly, combination of TrigToExp and GeneratedParameters -> (2 C[#] &) can realize the expected output. However, I actually want a pure option of DSolve that can do the job.
• The arbitrary constants are arbitrary so you can change them at will. (DSolve[y''[x] + y[x] == 0, y[x], x][[1]] // TrigToExp) /. {C[1] :> 2 C[1], C[2] :> 2 C[2]} – Bob Hanlon Oct 31 '16 at 5:19
• eqn = y''[x] + y[x] == 0; soln = DSolve[eqn, y, x, GeneratedParameters -> (2 C[#] &)][[1]] // TrigToExp; eqn /. soln evaluates to True – Bob Hanlon Oct 31 '16 at 6:18