Differential Equations

Let \(\alpha x=\exp \left(x^{\beta} y^{\gamma}\right)\) be the solution of the differential equation \(2 x^{2} y \mathrm{~d} y-\left(1-x y^{2}\right) \mathrm{d} x=0, x > 0,y(2)=\sqrt{\log _{e} 2}\). Then \(\alpha+\beta-\gamma\) equals :