The number of arbitrary constants in the particular solution of a differential equation of third order is:

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

The order and degree of the differential equation $\left(y^{\prime \prime \prime}\right)^3+\left(y^{\prime \prime}\right)^4+\left(y^{\prime}\right)^4+y=7$ are . . . . . . respectively.

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

The order and degree of the differential equation $e^{\frac{d^2 y}{d x^2}} = x$ are . . . . . . respectively.

The order and degree of the differential equation of all tangent lines to the parabola $x^2 = 4y$ are respectively: