Differential equation of plane rotator

Question

Just reflecting.

I'm studying plane rotator. My Teacher and my book say that the solution of $ -{\hbar^2 \over {2I}} {d^2\over{dx^2}} \psi_n(\phi)=E_n\psi$

is

$\psi_n(\phi)= C e^ {i\pm {\sqrt {2IE \over\hbar^2}}\phi}$.

Shouldn't the solution be in this form?

$\psi_n(\phi)= C_1 e^ {i {\sqrt {2IE_n \over\hbar^2}}\phi} +C_2 e^ {-i {\sqrt {2IE_n \over\hbar^2}}\phi} $.

I'm sure I'm just confused at the moment but I can't see the reason.

Thanks in advance.