The order and degree of the differential equation $\frac{d^3 y}{d x^3} = \left[1 + \left(\frac{d y}{d x}\right)^2\right]^{5/2}$ are respectively:

The degree of the differential equation ${\left( {1 + {{\left( {\frac{{dy}}{{dx}}} \right)}^2}} \right)^{3/4}} = {\left( {\frac{{{d^2}y}}{{d{x^2}}}} \right)^{1/3}}$ is

The sum of the order and degree of the differential equation $\frac{d^4 y}{d x^4}=\{c+(\frac{d y}{d x})^2\}^{\frac{3}{2}}$ is

Assertion $(A)$: The order of the differential equation of a family of circles with a constant radius is $2$.
Reason $(R)$: An algebraic equation having two arbitrary constants is the general solution of a second-order differential equation.

The order of the differential equation,whose general solution is given by $y = (c_1 + c_2) \cos (x + c_3) - c_4 e^{x + c_5}$,where $c_1, c_2, c_3, c_4$ and $c_5$ are arbitrary constants,is

The order and degree of the differential equation $\frac{d^2y}{dx^2} = \sqrt{1 + \left(\frac{dy}{dx}\right)^2}$ are