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Differential Equations question

2023 · 11 Apr · Shift 1 · Q29

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JEE Main
Mathematics
Differential Equations
2023 · 11 Apr · Shift 1 · Q29

Differential Equations question

2023 · 11 Apr · Shift 1 · Q29

JEE MainMathematicsDifferential EquationsMCQ+4 / −1

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 :

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

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