Assertion (A) The degree of the differential equation $y^{\prime \prime}+2 x y^{\prime}+\log _e\left(\frac{d y}{d x}\right)=0$ is 2 .

Reason (R) The degree of a differential equation is the highest degree of the highest order derivative occurring in the equation, after the equation is expressed in the form of a polynomial in differential coefficients. The correct option among the following

Let $S$ be the family of curves given by the general solution of the differential equation $\frac{y^2 e^{-1 / y}}{\sqrt{x}} d x-2 \sec \sqrt{x} d y=0$. Then, the equation of the curve belonging to $S$ and passing through $\left(\pi^2, 1\right)$ is

Statement I The differential equation corresponding to the family of circles having their centres on $Y$-axis and fixed radius $k$ is $\left(x^2-k^2\right)\left(\frac{d y}{d x}\right)^2+x^2=0$

Statement II The differential equation corresponding to the family of circles passing through the origin and having their centres on $X$-axis is $x^2-y^2+2 x y \frac{d y}{d x}=0$

Which of the above statements is (are) true?

If $m$ and $n$ are respectively the order and the degree of the differential equation representing the family of curves $y^2-5 a x-5 a^{3 / 2}=0(a>0$ is a parameter), then the value of $m-n$ is