Question
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 :
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 :