The differential equation for $y=A \cos (\alpha x)+B \sin (\alpha x)$, where A and B are arbitrary constants is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → $\frac{d^2 y}{d x^2}+\alpha^2 y=0$
No. of arbitrary constants = 2
So order → 2
So $\frac{dy}{dx}=α(-A\sin(αx)+\cos(αx))$
or $\frac{d^2y}{dx^2}=α^2(-A\sin(αx)-\cos(αx))$
$\frac{d^2y}{dx^2}=-α^2y$ or $\frac{d^2y}{dx^2}+α^2y=0$