# Solving ODE with Complex eigenvalue

For example, 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 $\pm i$ so general solution is $f(x) = c_1 e^{ix}+ c_2 e^{-ix}$ according to Euler's formula $$f(x) = c_1(\cos x+i\sin x) + c_2(\cos x-i\sin x )$$ it is different from the general solution generated by MAPLE why?

Thanks!

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