Question

The differential equation of the family of curves $y=acos(x+b)$ is

[MP PET 1993]

• A. $\frac{d^{2}y}{d{x}^2}-y=0$
• B. $\frac{d^{2}y}{d{x}^2}+y=0$
• C. $\frac{d^{2}y}{d{x}^2}+2y=0$
• D. None of these

Answer 1

The correct option is B

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

Given equation y = a cos (x + b)
Differentiate it w.r.t x we get $\frac{dy}{dx}=-asin(x+b)$
Again $\frac{d^{2}y}{d{x}^2}=-acos(x+b)=-yor\frac{d^{2}y}{d{x}^2}+y=0.$