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Let y=y(x) be a solution curve of the di...

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

`(3e^2)/(2(3e^2+1)`

B

`(3e^2)/(2(3e^2-1)`

C

`(1+3e^2)/(2(3e^2+1)`

D

`(1-3e^2)/(2(3e^2+1)`

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