The order and degree of differential equation $\sqrt[3]{2 y+\frac{d y}{d x}}=\left(x+\frac{d^3 y}{d x^3}\right)$ respectively are:

3, 3

The correct answer is Option (2) → 3, 3

$\sqrt[3]{2 y+\frac{d y}{d x}}=\left(x+\frac{d^3 y}{d x^3}\right)$

$⇒\left(2y+\frac{d y}{d x}\right)^3=\left(x+\frac{d^3 y}{d x^3}\right)^3$

$=x^3+\left(\frac{d^3 y}{d x^3}\right)^3+3x\frac{d^3 y}{d x^3}\left(x+\frac{d^3 y}{d x^3}\right)$

∴ Order = Highest order derivative = 03

Degree = Power of highest order derivative = 03