Differential equation, hint $$x^2y'^2-2(xy-2)y' +y^2=0$$ 
I have tried to determine y' using x, y
$$y'=-\frac{{\sqrt{1-xy}-1}^2}{x^2}$$
And I don't know what to do next. 

As a good start, let $y = vx$.  The equation in terms of $v$ and $x$ looks a lot simpler; something like 
$$x^4 v'^2 + 4x v' +4v = 0$$
Then a substitution of a form like $v = w + 2 x^{-3}$ gives something like
$$
w'^2 = f(x)
$$
which you can solve the way you started trying to solve the original.
