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Let y = y ( x ) be a solution curve of the differential equation, \(\left(1-{\mathrm{x}}^{2}{\mathrm{y}}^{2}\right)\math…

Q1

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

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

a

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

b

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

c

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

d

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

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