If the solution curve \( y=y(x) \) of the differential equation \( y^{2} d x+\left(x^{2}-x y+y^{...

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If the solution curve \( y=y(x) \) of the differential equation \( y^{2} d x+\left(x^{2}-x y+y^{2}\right) d y=0 \), 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
(a) \( \frac{\pi}{3} \)
(b) \( \frac{\pi}{2} \)
(c) \( \frac{\pi}{12} \)
(d) \( \frac{\pi}{6} \)
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