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