The order of the differential equation of all circles whose radius is $4$,is . . . . . .

The order of the differential equation corresponding to the family of parabolas whose axes are along the $X$-axis and whose foci are at the origin,is

If $m$ and $n$ are 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 obtained by eliminating the arbitrary constants $a$ and $b$ from $xy = ae^x + be^{-x}$ is

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

The differential equation of all straight lines passing through the point $(1, -1)$ is