The differential equation $x(\frac{d^2y}{dx^2})^3 + (\frac{dy}{dx})^4 + y = x^2$ is of

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

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

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