JEE Math Practice 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

1. A.$${1 \over 2}\exp \left( {{\pi \over 6} + \sqrt e - 1} \right)$$
2. B.$${1 \over 2}\exp \left( {{\pi \over 6} + e - 1} \right)$$
3. C.$$\exp \left( {{\pi \over 6} + \sqrt e + 1} \right)$$
4. D.$$2\exp \left( {{\pi \over 3} + \sqrt e - 1} \right)$$