Solve the differential equation : `(1-x^2)(1-y)\ dx=x y(1+y)dy`

Explanation

`(1-x^(2))(1-y)dx=xy(1+y)dy`
`implies ((1-x^(2)))/(x)dx=(y(1+y))/((1-y))dy`
`implies((1)/(x)-x)dx=(-y-2+(2)/(1-y))dy`
`implies int ((1)/(x)-x)dx=int(-y-2+(2)/(1-y))dy+c`
`implies logx-(x^(2))/(2)=-(y^(2))/(2)-2y-2log(1-y)+c`
`implies logx+2log(1-y)=(x^(2))/(2)-(y^(2))/(2)-2y+c`
`implies log{x(1-y)^(2)}=(1)/(2)[x^(2)-y^(2)]-2y+c`.