Determine the order and the degree of the equation $\frac{d^3y}{dx^3}+x^2\left(\frac{d^2y}{dx^2}\right)^3=0$.
Answer & explanation
Correct answer: option 3
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.