For the differential equation $xy\large\frac{dy}{dx}=$$(x+2)(y+2),$ find the solution curve passing through the point $(1,-1)$.

Question

$\begin{array}{1 1}y - x +2 = log(x^2)(y+2)^2 \\ y+ x +2 = log(x^2)(y-2)^2 \\ y - x - 2 = log(x^2)(y-2)^2 \\ y + x +2 = log(x^2)(y+2)^2 \end{array}$