By eliminating the arbitrary constants from $y=(a+b) \sin (x+c)-d e^{x+e+f}$,the differential equation obtained is of order

The differential equation representing the family of parabolas having vertex at the origin and axis along the positive $Y$-axis is

The differential equation of all parabolas,whose axes are parallel to the $Y$-axis,is

The differential equation whose solution is $(x - h)^2 + (y - k)^2 = a^2$ is ($a$ is a constant).

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.

The differential equation for the family of curves ${x^2} + {y^2} - 2ay = 0,$ where $a$ is an arbitrary constant,is