If the solution curve y = y(x) of the differential equation y²dx + (x² - xy + y²)dy = 0, which passes through the point (1, 1) and intersects the line y = 3 x at the point (α, 3 α), then value of log e (3 α) is equal to:

Differential Equations: JEE Main 2022 Mathematics question

JEE Main 2022 · 25 Jun, Morning shift · Q3626

JEE Main 202225 Jun, Morning shiftMathematicsMediumDifferential Equations163× since 2002

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 :