Let $\displaystyle \phi (x)$ be a solution of the second order linear differential equation

$\displaystyle y^{''}+(sin x)^{2}y^{'}+y=0$defined on $\displaystyle \mathbb{R}$ satisfying $\displaystyle \phi (0)=\phi (\pi)$ and $\displaystyle \phi^{'} (0)=\phi^{'} (\pi)$. Prove that $\displaystyle \phi (x+\pi)=\phi (x)$ for all $\displaystyle x \in \mathbb{R}$.

How do I go about doing it?