The sum of order and degree of the differential equation $\frac{\left\{1+\left(\frac{d y}{d x}\right)^2\right\}^{\frac{5}{2}}}{\frac{d^2 y}{d x^2}}=p$ is:

4

The correct answer is Option (3) - 4

$\left\{1+\left(\frac{dy}{dx}\right)^2\right\}^{\frac{5}{2}}=p\frac{d^2 y}{d x^2}$

Squaring both sides

$(1+(\frac{dy}{dx})^2)^5=p^2(\frac{d^2 y}{d x^2})^2$

order = 2, degree = 2

sum = 2 + 2 = 4