If the order and degree of the differential equation corresponding to the family of curves $y^2=4a(x+a)$ (where $a$ is a parameter) are $m$ and $n$ respectively, then $m+n^2=$

The differential equation of $y=ae^{bx}$ (where $a$ and $b$ are parameters) is:

The order of the differential equation obtained by eliminating arbitrary constants in the family of curves $c_{1} y = (c_{2} + c_{3}) e^{x + c_{4}}$ is

The differential equation of the family of all circles of radius $a$ is

Statement $(I)$: The elimination of arbitrary constants $\alpha, \beta$ and $\gamma$ from $y=(\alpha+\beta+\gamma) x$ results in a differential equation of order three.
Statement $(II)$: The elimination of arbitrary constants $\alpha, \beta$ and $\gamma$ from $y=\alpha x+\beta \sin x+\gamma e^x$ results in a differential equation of order three.

The order of the differential equation whose solution is $y=a \cos x+b \sin x+c e^{-x}$ is