Determine the order and the degree of the equation $\frac{d^3y}{dx^3}+x^2\left(\frac{d^2y}{dx^2}\right)^3=0$.

Order = 3, Degree = 1

The correct answer is Option (3) → Order = 3, Degree = 1

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

The highest order derivative present in the given differential equation is $\frac{d^3y}{dx^3}$, so its order is 3. Here each term in the derivative is a polynomial, so its degree is the highest exponent of $\frac{d^3y}{dx^3}$ which is 1. Thus, its degree is 1.

Hence, the order is 3 and degree is 1.