Question

Find the order and degree of the differential equation $\sqrt{1-{\left(\frac{dy}{dx}\right)}^2}=a{\left(\frac{d^{2}y}{d{x}^2}\right)}^{\frac{1}{3}}$ .

Answer 1

On squaring

$1-{\left(\frac{dy}{dx}\right)}^2=a{\left(\frac{d^{2}y}{d{x}^2}\right)}^{\frac{1}{3}}\Rightarrow {[1-{\left(\frac{dy}{dx}\right)}^2]}^3{a}^3=\frac{d^{2}y}{d{x}^2}$

Order = 2, degree = 1