Question

$y=a\cos x+b\sin x$ is the solution of which of the differential equation.

• A. $\frac{d^{2}y}{d{x}^2}+y=0$
• B. $\frac{d^{2}y}{d{x}^2}-y=0$
• C. $\frac{dy}{dx}+y=0$
• D. $\frac{dy}{dx}+x\frac{dy}{dx}=0$

Answer 1

The correct option is A $\frac{d^{2}y}{d{x}^2}+y=0$

$y=acosx+bsinx$

$⟹\frac{dy}{dx}=-asinx+bcosx⟹\frac{d^{2}y}{d{x}^2}=-acosx-bsinx⟹\frac{d^{2}y}{d{x}^2}=-y⟹\frac{d^{2}y}{d{x}^2}+y=0$