The order of the differential equation of the family of all concentric circles centered at $(h, k)$ is

The equation which represents the system of parabolas whose axis is parallel to the $y$-axis satisfies the differential equation:

If $m$ and $n$ are respectively the order and degree of the differential equation of the family of parabolas with focus at the origin and $X$-axis as its axis,then $m n-m+n=$

The differential equation of the family of curves $r^2 = a^2 \cos 2\theta$,where '$a$' is an arbitrary constant,is:

The differential equation of all the ellipses centered at the origin and having axes as the coordinate axes is

The differential equation whose solution is $y = cx + c - c^3$ is: