Differential Equations

Let \(y=y(x)\) be a solution curve of the differential equation.

\(\left(1-x^{2} y^{2}\right) d x=y d x+x d y\).

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 :