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ODE: y'' + y = 0

solve this problem using MAPLE

f(x) = _C1*sin(x)+_C2*cos(x)

My question is Eigenvalue for D^2+1=0 is +i, -i

so general solution is f(x) = C1*exp(i*x)+C2*exp(-i*x)

according to Euler's formula f(x) = C1( cos(x)+i*sin(x) ) + C2*( cos(x)-i*sin(x) )

it is different from the general solution generated by MAPLE

why?

Thanks!