The order of the differential equation of a family of curves represented by an equation containing four arbitrary constants will be:

The differential equation for which $y^2 = 4a(x + a)$ (where $a$ is a parameter) is the general solution, is

If $m$ and $n$ are respectively the order and the degree of the differential equation representing the family of curves $y^2 - 5ax - 5a^{3/2} = 0$ ($a > 0$ is a parameter), then the value of $m - n$ is

The differential equation of $y=e^x(a \cos x+b \sin x)$ is

The normal form of the equation of a straight 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.

The differential equation of the family of straight lines whose slope is equal to $y$-intercept is