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:
