Let $$y = y(x)$$ be a solution curve of the differential equation, $$(1 - x^2y^2)dx = ydx + xdy$$. If the line $$x = 1$$ intersects the curve $$y = y(x)$$ at $$y = 2$$ and the line $$x = 2$$ intersects the curve $$y = y(x)$$ at $$y = \alpha$$, then a value of $$\alpha$$ is

A

$$\frac{1-3e^2}{2(3e^2+1)}$$

B

$$\frac{1+3e^2}{2(3e^2-1)}$$

C

$$\frac{3e^2}{2(3e^2+1)}$$

D

$$\frac{3e^2}{2(3e^2-1)}$$