Let α x= exp (x^β y^γ) be the solution of the differential equation 2 x^2 y d y-(1-x y^2) d x=0, x>0, y(2)=√(log_e 2). Then α+β-γ equals:

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