The product of order and degree of the differential equation $\left(\frac{d^3y}{dx^3}\right)^2+x^2y\left(\frac{d^2y}{dx^2}\right)^3=2x^5$ is:

6

The correct answer is Option (2) → 6

Given differential equation:

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

Order is the highest order derivative: $ \frac{d^3 y}{dx^3} $ ⇒ Order = 3

Degree is the highest power of the highest order derivative when equation is polynomial in derivatives ⇒ Degree = 2

Required product = Order × Degree = 3 × 2 = 6