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