Q. The differential equation of the family of curves $y = a\cos{(x + b)}$ is
A) $\frac{d^{2}y}{dx^{2}} - y = 0$
B) $\frac{d^{2}y}{dx^{2}} + y = 0$
C) $\frac{d^{2}y}{dx^{2}} + 2y = 0$
D) None of these
Explanation
(b)
Given, $y = {acos}{(x + b)}$
$\Rightarrow$ $\frac{dy}{dx} = - {asin}{(x + b)}$
$\Rightarrow$ $\frac{d^{2}y}{dx^{2}} = - {acos}{(x + b)} = - y$
$\Rightarrow$ $\frac{d^{2}y}{dx^{2}} + y = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.