If $$x \frac{dy}{dx} = y(\log y - \log x + 1)$$, then the solution of the equation is

A

$$y \log\left(\frac{x}{y}\right) = cx$$

B

$$x \log\left(\frac{y}{x}\right) = cy$$

C

$$\log\left(\frac{y}{x}\right) = cx$$

D

$$\log\left(\frac{x}{y}\right) = cy$$