The differential equation for $y=A \cos (\alpha x)+B \sin (\alpha x)$, where A and B are arbitrary constants is:

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

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

The correct answer is Option (1) → $\frac{d^2 y}{d x^2}+\alpha^2 y=0$