Let y {\displaystyle y} be the solution to the differential equation d y d x = cos x 2 y {\displaystyle {\frac {dy}{dx}}={\frac {\cos x}{2y}}} satisfying y ( 0 ) = 3 . {\displaystyle y(0)={\sqrt {3}}.} What is y ( π 2 ) {\displaystyle y\left({\frac {\pi }{2}}\right)} ? Simplify your answer completely.
