JEE Math Practice Question

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 :

1. A.$$\frac{1+3 e^{2}}{2\left(3 e^{2}-1\right)}$$
2. B.$$\frac{3 e^{2}}{2\left(3 e^{2}-1\right)}$$
3. C.$$\frac{1-3 e^{2}}{2\left(3 e^{2}+1\right)}$$
4. D.$$\frac{3 e^{2}}{2\left(3 e^{2}+1\right)}$$