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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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