Question Id : 14184 |
Context : JEE Main 2024 (29 January Evening Shift)
If $\sin\!\left(\dfrac{y}{x}\right)=\log_e|x|+\dfrac{\alpha}{2}$
is the solution of the differential equation
$x\cos\!\left(\dfrac{y}{x}\right)\dfrac{dy}{dx}=y\cos\!\left(\dfrac{y}{x}\right)+x$
and $y(1)=\dfrac{\pi}{3}$, then $\alpha^{2}$ is equal to:
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