The differential equation of the family of curves represented by the equation ${x^2} + {y^2} = {a^2}$ is

The differential equation of the family of curves ${y^2} = 4a(x + a)$,where $a$ is an arbitrary constant,is

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

The differential equation whose solution represents the family $x^2 y = 4e^x + c$,where $c$ is an arbitrary constant,is

Statement $I$: The differential equation corresponding to the family of circles having their centres on $Y$-axis and fixed radius $k$ is $(x^2-k^2)(\frac{dy}{dx})^2+x^2=0$.
Statement $II$: The differential equation corresponding to the family of circles passing through the origin and having their centres on $X$-axis is $x^2-y^2+2xy \frac{dy}{dx}=0$.
Which of the above statements is (are) true?

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 $m n-m+n=$