The number of arbitrary constants in the particular solution of a fourth-order differential equation is . . . . . . .

Find the degree of the differential equation $y_3^{2/3} + 2 + 3y_2 + y_1 = 0$.

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

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 $\frac{d^2 y}{d x^2}+y+\left(\frac{d y}{d x}-\frac{d^3 y}{d x^3}\right)^{3 / 2}=0$ are respectively:

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