Solution
= Solution
The characteristic <polynomial> after multiplication by four is $r^2+4r+4+\pi^2$, with roots $-2\pm i\pi$. Thus the general real solution of this constant-coefficient <ordinary differential equation> is
$$
\boxed{y(x)=e^{-2x}[A\cos(\pi x)+B\sin(\pi x)],\qquad A,B\in\mathbb R.}
$$
Equivalently the <change of dependent variable> $y=e^{-2x}v$ gives $Ly=\tfrac14e^{-2x}(v''+\pi^2v)$.