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

The order of the differential equation whose solution is $a e^{x} + b e^{2x} + c e^{3x} + d = 0$ is:

The degree of the differential equation whose solution is $y^2=8a(x+a)$ is

If $\alpha$ and $\beta$ are respectively the order and degree of the differential equation for which $a x^2+b y^2=1$ is the general solution, then the eccentricity of the ellipse $\alpha x^2+\beta y^2=1$ is

The differential equation of the family of curves $y = a e^x + b x e^x + c x^2 e^x$,where $a, b, c$ are arbitrary constants,is

The differential equation corresponding to the family of ellipses $\frac{x^2}{a^2} + \frac{y^2}{4} = 1$, where '$a$' is an arbitrary constant, is: