Q. The order of the differential equation $\frac{d^{2}y}{dx^{2}} = \sqrt{1 + \left( \frac{dy}{dx} \right)^{2}}$ is
A) $3$
B) $2$
C) $1$
D) $4$
Explanation
(b)
Given differential equation is
$\frac{d^{2}y}{dx^{2}} = \sqrt{1 + \left( \frac{dy}{dx} \right)^{2}}$
$\Rightarrow$ $\left( \frac{d^{2}y}{dx^{2}} \right)^{2} = 1 + \left( \frac{dy}{dx} \right)^{2}$
Hence, order is 2.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.