The order and degree of the differential equation $\left[\left(\frac{d^2 y}{d x^2}\right)^2-3\right]^{\frac{1}{3}}=2\left(\frac{d y}{d x}\right)^{\frac{1}{4}}$ are

order = 2, degree = 8

Raising equation to power of 12 we get

$\left(\left(\frac{d^2 y}{d x^2}\right)^2-3\right)^4=2\left(\frac{d y}{d x}\right)^3$

⇒ Order = 2

Degree = 2 × 4 = 8 (Degree $\frac{d^2 y}{d x^2}$ × power to which expression is raised)