Find the sum of the order and the degree of the following differential equation $\left(\frac{d^2y}{dx^2}\right)^2+\left(\frac{dy}{dx}\right)^3+x^4=0$.

4

The correct answer is Option (3) → 4

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 2. Thus, its degree is 2.

∴ The sum of the order and the degree of the given differential equation $=2+2=4$.