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

The given differential equation

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

can be written as

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

From the equation it is clear second order derivative involved in the equation, so the order is $2$ and power of the highest ordered term is $2$ so the degree of the differential equation is $2$.