JEE Math Practice Question

If the solution curve $$y = y(x)$$ of the differential equation $${y^2}dx + ({x^2} - xy + {y^2})dy = 0$$, which passes through the point (1, 1) and intersects the line $$y = \sqrt 3 x$$ at the point $$(\alpha ,\sqrt 3 \alpha )$$, then value of $${\log _e}(\sqrt 3 \alpha )$$ is equal to :

1. A.$${\pi \over 3}$$
2. B.$${\pi \over 2}$$
3. C.$${\pi \over 12}$$
4. D.$${\pi \over 6}$$