The order of the differential equation $\left(\frac{d^3 y}{d x^3}\right)^4+\left(\frac{d^2 y}{d x^2}\right)^2+\sin \left(\frac{d y}{d x}\right)+1=0$ is . . . . . . .

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 . . . . . . .

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 degree of the differential equation $y = a(1 - e^{-x/a})$,where $a$ is a parameter,is:

The order of the differential equation whose general solution is $y = a_1(a_2 + a_3) \cdot \cos(x + a_4) - a_5 e^{x + a_6}$ is . . . . . . .

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