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

Find the order and degree,if defined,of the following differential equation:
$x y \frac{d^{2} y}{d x^{2}}+x\left(\frac{d y}{d x}\right)^{2}-y \frac{d y}{d x}=0$

Assertion $(A)$: The degree of the differential equation $y'' + 2xy' + \log_e\left(\frac{dy}{dx}\right) = 0$ is $2$.
Reason $(R)$: The degree of a differential equation is the highest power of the highest order derivative occurring in the equation, after the equation is expressed in the form of a polynomial in differential coefficients.
The correct option among the following is:

The order and degree of the differential equation $(\frac{d^3y}{dx^3})^{\frac{2}{3}} - 3\frac{d^2y}{dx^2} + 5\frac{dy}{dx} + 4 = 0$ are respectively:

The degree of the differential equation $\frac{d^2y}{dx^2} + \left( \frac{dy}{dx} \right)^3 + 6y = 0$ is

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