The differential equation for which $y=a \cos x+b \sin x$ is a solution, is

$\frac{d^2 y}{d x^2}+y=0$ $\frac{d^2 y}{d x^2}-y=0$ $\frac{d^2 y}{d x^2}+(a+b) y=0$ $\frac{d^2 y}{d x^2}+(a-b) y=0$

$\frac{d^2 y}{d x^2}+y=0$

We have, $y=a \cos x+b \sin x$ $\Rightarrow \frac{d y}{d x}=-a \sin x+b \cos x$ $\Rightarrow \frac{d^2 y}{d x^2}=-a \cos x-b \sin x \Rightarrow \frac{d^2 y}{d x^2}=-y$