Answer
$$y = {\sin ^{ - 1}}\left( {\frac{x}{2}} \right) + \pi $$
Work Step by Step
$$\eqalign{
& \frac{{dy}}{{dx}} = \frac{1}{{\sqrt {4 - {x^2}} }} \cr
& {\text{Separating variables}} \cr
& dy = \frac{1}{{\sqrt {4 - {x^2}} }}dx \cr
& {\text{Integrating both sides}} \cr
& \int {dy} = \int {\frac{1}{{\sqrt {4 - {x^2}} }}} dx \cr
& y = {\sin ^{ - 1}}\left( {\frac{x}{2}} \right) + C{\text{ }}\left( {\bf{1}} \right) \cr
& {\text{Using the initial condition }}y\left( 0 \right) = \pi \cr
& \pi = {\sin ^{ - 1}}\left( {\frac{0}{2}} \right) + C \cr
& C = \pi \cr
& {\text{Substituting }}C{\text{ into }}\left( {\bf{1}} \right) \cr
& y = {\sin ^{ - 1}}\left( {\frac{x}{2}} \right) + \pi \cr} $$
