The sum of order and degree of the differential equation $\left(x^2\frac{d^2y}{dx^2}\right)^{3/4}= 5(\frac{dy}{dx})^2- 3$ is equal to

5

The correct answer is Option (3) → 5

Given differential equation:

$\left(x^{2}\frac{d^{2}y}{dx^{2}}\right)^{\frac{3}{4}} = 5\left(\frac{dy}{dx}\right)^{2} - 3$

To make it a polynomial in derivatives, raise both sides to the power $\frac{4}{3}$:

$x^{2}\frac{d^{2}y}{dx^{2}} = \left(5\left(\frac{dy}{dx}\right)^{2} - 3\right)^{\frac{4}{3}}$

Highest order derivative: $\frac{d^{2}y}{dx^{2}} \Rightarrow$ Order = 2

Degree = 3 (power of highest derivative after removing radicals/fractions)

Sum of order and degree = $2 + 3 = 5$

Sum = 5