If $\sin \left( \frac { y } { x } \right) = \log _ { e } | x | + \frac { \alpha } { 2 }$ is the solution of the differential equation $x \cos \left( \frac { y } { x } \right) \frac { d y } { d x } = y \cos \left( \frac { y } { x } \right) + x$ and $y ( 1 ) = \frac { \pi } { 3 }$, then $\alpha ^ { 2 }$ is equal to\\
(1) 3\\
(2) 12\\
(3) 4\\
(4) 9