The differential equation which represents the family of curves $y = C_1 e^{C_2 x}$,where $C_1$ and $C_2$ are arbitrary constants,is:

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

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

Form the differential equation representing the family of ellipses having foci on the $x$-axis and centre at the origin.

Verify that the given function $y=\sqrt{1+x^{2}}$ is a solution of the differential equation $y^{\prime}=\frac{xy}{1+x^{2}}$.

If the order of a differential equation $\frac{d^2 y}{d x^2}-2\left(\frac{d y}{d x}\right)^3+\sin \left(\frac{d y}{d x}\right)+y=0$ is $l$ and the degree of the differential equation $\left(1+\frac{d^2 y}{d x^2}\right)^{\frac{2}{3}}=\left[2-\left(\frac{d y}{d x}\right)^3\right]^{\frac{3}{2}}$ is $m$, then the differential equation corresponding to the family of curves $y=A x^l+B e^{m x}$, where $A$ and $B$ are arbitrary constants, is