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

2

The correct answer is Option (3) → 2

The given differential equation $x^3\left(\frac{d^2y}{dx^2}\right)^2+x\left(\frac{dy}{dx}\right)^4=0$.

The highest order derivative present in the given differential equation is $\frac{d^2y}{dx^2}$ and 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, the degree of the given differential equation is 2.