Question

State whether the statement is true/false.

If $y=a\sin x+b\cos x$, then $\frac{d^{2}y}{d{x}^2}+y=0$

• A. True
• B. False

Answer 1

The correct option is A True

$y=a\sin x+b\cos x$

$\frac{dy}{dx}=a\cos x-b\sin x$

$\frac{d^{2}y}{d{x}^2}=-a\sin x-b\cos x$

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

$\Rightarrow \frac{d^{2}y}{d{x}^2}=-y$

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

Hence the given statement is true.