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

2

The correct answer is Option (4) → 2

Given differential equation:

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

Remove the fractional exponent by squaring both sides:

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

$\left( 2 + \left( \frac{dy}{dx} \right)^2 \right)^3 = a^4 \left( \frac{d^2 y}{dx^2} \right)^2$

The highest order derivative is $\frac{d^2 y}{dx^2}$, and its power is $2$.