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

y= 2 sin(x +C) y= 2 cos(x +C) y= 2 tan(x +C) y= 2 cot (x +C)

y= 2 sin(x +C)

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)