If sin (y/x)= log_e|x|+(α)/2 is the solution of the differential equation x cos (y/x) (d y)/(d x)=y cos (y/x)+x and y(1)=(π)/3, then α^2 is equal to

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