The differential equation representing the family of curves $y^{2}=2 d(x+\sqrt{d})$, where $d$ is a parameter, is of

The degree of the differential equation $\left(\frac{d^2 y}{d x^2}\right)^5+\left(\frac{d y}{d x}\right)^2+\cos \left(\frac{d y}{d x}\right)+1=0$ is . . . . . . .

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

For the differential equation $\sqrt{\frac{d^2 y}{d x^2}}=\sqrt[3]{\left[y \frac{d y}{d x}+x \sin \left(\frac{d y}{d x}\right)\right]^2}$, find the order and degree.

Assertion $(A)$: The order of the differential equation of a family of circles with a constant radius is $2$.
Reason $(R)$: An algebraic equation having two arbitrary constants is the general solution of a second-order differential equation.

The order and the degree of the differential equation $\frac{d^4y}{dx^4} - 4\frac{d^3y}{dx^3} + 8\frac{d^2y}{dx^2} - 8\frac{dy}{dx} + 4y = 0$ are respectively: