The degree of the differential equation $\left[ 1 + \left( \frac{dy}{dx} \right)^2 \right]^{3/2} = \frac{d^2y}{dx^2}$ is

2

The correct answer is Option (4) → 2 ##

Given that $\left[ 1 + \left( \frac{dy}{dx} \right)^2 \right]^{3/2} = \frac{d^2y}{dx^2}$

On squaring both sides, we get

$\left[ 1 + \left( \frac{dy}{dx} \right)^2 \right]^3 = \left( \frac{d^2y}{dx^2} \right)^2$

The highest order derivative is $\frac{d^2y}{dx^2}$ and the highest power raised to $\frac{d^2y}{dx^2}$ is 2.

So, the degree of differential equation is 2.