Find the general solution of the following differential equations
`(dy)/(dx) = sqrt(4 - y^2) (-2 lt y lt 2)`

Explanation

`(dy)/(dx) = sqrt(4-y^2)`
`(dy)/sqrt(4-y^2) = dx`
`(dy)/sqrt(2^2 - y^2) = dx`
`therefore` The general solution is `int (dy)/sqrt(2^2 - y^2) = int dx + c `
`sin^-1 (y/2) = x + c`
y/2 = sin(x + c)
i.e, y = 2sin (x + c)