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

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 of all tangent lines to the parabola $x^2 = 4y$ are respectively:

The order and degree of the differential equation $\frac{d^2y}{dx^2} + \left( \frac{dy}{dx} \right)^{1/3} + x^{1/4} = 0$ are respectively:

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

The order and degree of the differential equation $\sqrt{1+\frac{1}{(\frac{dy}{dx})^2}} = (\frac{d^2y}{dx^2})^{3/2}$ are respectively: