Answer
$$ y= \sin^{-1}(e^{x-\ln 2})= \sin^{-1}(e^{x}/2).$$
Work Step by Step
By separation of variables, we have
$$\frac{\cos y}{\sin y}dy=dx $$
then by integration, we get
$$ \ln(\sin y)=x+c .$$
Now, since $y(\ln 2)=\pi/2$, then $c=-\ln 2$.
So the general solution is given by $$ y= \sin^{-1}(e^{x-\ln 2})= \sin^{-1}(e^{x}/2).$$
