Let $y = y(x)$ be a solution curve of the differential equation \[ (1 - x^2 y^2)\,dx = y\,dx + x\,dy. \] 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: