Question

Consider the differential equation $\frac{d^{2}y}{d{x}^2}={(1+\frac{dy}{dx})}^{2/3}$. Find the degree and order of the equation.

Answer 1

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

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

$⟹{\left(\frac{d^{2}y}{d{x}^2}\right)}^3-{\left(\frac{dy}{dx}\right)}^2-2\frac{dy}{dx}-1=0$

$⟹$ Degree=3, Order=2