Differential Equations: JEE Main 2022 Mathematics question

Let the solution curve $y = y(x)$ of the differential equation $\left[ {{x \over {\sqrt {{x^2} - {y^2}} }} + {e^{{y \over x}}}} \right]x{{dy} \over {dx}} = x + \left[ {{x \over {\sqrt {{x^2} - {y^2}} }} + {e^{{y \over x}}}} \right]y$ pass through the points (1, 0) and (2$\alpha$, $\alpha$), $\alpha$ > 0. Then $\alpha$ is equal to