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 $m^2+n=$

Consider the differential equation $\frac{d y}{d x}=\frac{1}{a x+4 y+7}$ and the following statements

A. The given differential equation is linear in $x$.

B. The given differential equation is not linear in $y$.

C. The given differential equation is linear in $y$.

D. $e^{a x}$ is the integrating factor of the given differential equation.

Which one of the following options is true?

The solution of the differential equation $x \cos x \frac{d y}{d x}+(x \sin x+\cos x) y=1$ 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