The order and degree of the differential equation $\sqrt{2 + (\frac{d^2y}{dx^2})^3} = (\frac{d^3y}{dx^3})^{5/2}$ are respectively:

The number of arbitrary constants in the particular solution of a differential equation of third order are . . . . . . .

If $m$ and $n$ are the order and degree of the differential equation $\left( \frac{d^2y}{dx^2} \right)^5 + 4\frac{\left( \frac{d^2y}{dx^2} \right)^3}{\left( \frac{d^3y}{dx^3} \right)} + \frac{d^3y}{dx^3} = x^2 - 1$,then

The degree of the differential equation $\left(\frac{d^{2} y}{d x^{2}}\right)^{3}+\left(\frac{d y}{d x}\right)^{2}+\sin \left(\frac{d y}{d x}\right)+1=0$ is

Find the order and degree,if defined,of the following differential equation:
$\frac{dy}{dx} - \cos x = 0$

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