If sin(y/x) = ln|x| + α/2 is the solution of the differential equ… | JEE Main 2024 Mathematics PYQ

MCQMediumJEE Main 2024 · 29 January, Shift 2Homogeneous Differential Equations

If $\sin\left(\frac{y}{x}\right) = \ln|x| + \frac{\alpha}{2}$ is the solution of the differential equation $x \cos\left(\frac{y}{x}\right) \frac{dy}{dx} = y \cos\left(\frac{y}{x}\right) + x$ , and $y(1) = \frac{\pi}{3}$ , then $\alpha^2$ is equal to:

A
$3$
B
$12$
C
$4$
D
$9$

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