Find the sum of the order and the degree of the following differential equation $y = x\left(\frac{dy}{dx}\right)^3+\frac{d^2y}{dx^2}$.

3

The correct answer is Option (2) → 3

The highest order derivative present in the given differential equation is $\frac{d^2y}{dx^2}$, so its order is 2. Here each term in the derivative is a polynomial, so its degree is the highest exponent of $\frac{d^2y}{dx^2}$ which is 1. Thus, its degree is 1.

∴ The sum of the order and the degree of the given differential equation $=2+1=3$.