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Let y=y(x) be a solution curve of the differential equation. \(\left(1-{x}^{2}{y}^{2}\right)dx=ydx+xdy\). If the line x …

Q1

Let y=y(x) be a solution curve of the differential equation. \(\left(1-{x}^{2}{y}^{2}\right)dx=ydx+xdy\). 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

[JEE Main 2023, 11 Apr (Shift 1)]

a

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

b

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

c

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

d

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

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