The solution of the differential equation dy/dx=√(4-y2) where (-2<y<2)

The given differential equation is dy/dx=√(4-y²) 

separating the variable, we get:

dy/(√(4-y²) = dx

Now, integrating both sides of this equation, we get:

∫{dy/(√(4-y²)} = ∫dx

⇒sin^-1 (y/2) = x + C

⇒ y= 2 sin(x +C)