Consider the differential equation, $x \frac{dy}{dx} = y(\log_e y - \log_e x + 1)$, then which of the following are true?
(A) It is a linear differential equation
(B) It is a homogenous differential equation
(C) Its general solution is $\log_e(\frac{y}{x}) = Cx$, where C is constant of integration
(D) Its general solution is $\log_e(\frac{x}{y}) = Cy$, where C is constant of integration
(E) If y(1) = 1, then its particular solution is y = x
Choose the correct answer from the options given below: