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Differential Equations question

2022 · 25 Jun · Shift 1 · Q36

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JEE Main
Mathematics
Differential Equations
2022 · 25 Jun · Shift 1 · Q36

Differential Equations question

2022 · 25 Jun · Shift 1 · Q36

JEE MainMathematicsDifferential EquationsMCQ+4 / −1

If the solution curve

y = y(x)

of the differential equation

{y^2}dx + ({x^2} - xy + {y^2})dy = 0

, which passes through the point (1, 1) and intersects the line

y = \sqrt 3 x

at the point

(\alpha ,\sqrt 3 \alpha )

, then value of

{\log _e}(\sqrt 3 \alpha )

is equal to :

A
${\pi \over 3}$
B
${\pi \over 2}$
C
${\pi \over 12}$
D
${\pi \over 6}$

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