The order and degree of the differential equation $(1+3\frac{dy}{dx})^{\frac{2}{3}}=4\frac{d^3y}{dx^3}$ respectively are :

$3, 3$

The correct answer is Option (4) → $3, 3$

$(1+3\frac{dy}{dx})^{\frac{2}{3}}=4\frac{d^3y}{dx^3}$

making powers in whole numbers

so $\left(1+3\frac{dy}{dx}\right)^2=4^3\left(\frac{d^3y}{dx^3}\right)^3$

order = 3, degree = 3