If y=A sin x+B cos x, then which of the following is correct?

The correct answer is Option (2) → $\frac{d^2 y}{d x^2}+y=0$

$y=A\sin x+B\cos x$   ...(1)

$⇒\frac{dy}{dx}=A\cos x-B\sin x$

$⇒\frac{d^2y}{dx^2}=-A\sin x-B\cos x$   ...(2)

∴ from (1) and (2),

$⇒\frac{d^2y}{dx^2}+y=0$