The differential equation for the line $y = mx + c$ is (where $m$ and $c$ are arbitrary constants).

The differential equation of the circles having their centres on the line $y=8$ and touching the $X$-axis is

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

The differential equation of the family of hyperbolas having their centres at the origin and their axes along the coordinate axes is

The order of the differential equation whose solution is $a e^{x} + b e^{2x} + c e^{3x} + d = 0$ is:

The normal form of the equation of a line is $x \cos \alpha + y \sin \alpha = p$. Find the differential equation of the family of all such lines, where $p$ and $\alpha$ are arbitrary constants.