Question

Find the order and degree of the differential equation ${\displaystyle {(1+3\frac{dy}{dx})}^{\frac{2}{3}}=4\left(\frac{d^{3}y}{{dx}^3}\right)}$.

Answer 1

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

Cubing both sides

${\displaystyle {(1+\frac{3dy}{dx})}^2=64{\left(\frac{d^{3}y}{{dx}^3}\right)}^3}$

∴ Order = 3,

Degree = 3