For the differential equation $\left(x \log _e x\right) d y=\left(\log _e x-y\right) d x$

(A) Degree of the given differential equation is 1.
(B) It is a homogeneous differential equation.
(C) Solution is $2 y \log _e x+A=\left(\log _e x\right)^2$, where A is an arbitrary constant.
(D) Solution is $2 y \log _e x+A=\log _e\left(\log _e x\right)$, where A is an arbitrary constant.

Choose the correct answer from the options given below:

(A) and (C) only

The correct answer is Option (1) → (A) and (C) only