Question

The differential equation representing the family of curves $y=A\cos (x+B)$, where $A,B$ are parameters, is

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

Answer 1

Answer: (A)

Since $y=A\cos (x+B)$
$\therefore \frac{dy}{dx}=-A\sin (x+B)$
$\Rightarrow \frac{d^{2}y}{d{x}^2}=-A\cos (x+B)=-y$
$\Rightarrow \frac{d^{2}y}{d{x}^2}+y=0$