\[ y'(x)=-\frac {y(x) (x y(x)+1)}{x (x y(x)-y(x)+1)} \] ✓ Mathematica : cpu = 12.1163 (sec), leaf count = 399
\[\text {Solve}\left [-\frac {\sqrt [3]{-2} \left (\frac {2^{2/3} ((x-1) y(x)-2)}{\sqrt [3]{-\frac {1}{(x-1)^3}} (x-1) ((x-1) y(x)+1)}+(-2)^{2/3}\right ) \left (\frac {-x y(x)+y(x)+2}{\sqrt [3]{2} \sqrt [3]{-\frac {1}{(x-1)^3}} (x-1) ((x-1) y(x)+1)}+(-2)^{2/3}\right ) \left (\left (\frac {\sqrt [3]{-1} (-x y(x)+y(x)+2)}{\sqrt [3]{-\frac {1}{(x-1)^3}} (x-1) ((x-1) y(x)+1)}+1\right ) \left (-\log \left (\frac {2^{2/3} ((x-1) y(x)-2)}{\sqrt [3]{-\frac {1}{(x-1)^3}} (x-1) ((x-1) y(x)+1)}+(-2)^{2/3}\right )\right )+\left (\frac {\sqrt [3]{-1} (-x y(x)+y(x)+2)}{\sqrt [3]{-\frac {1}{(x-1)^3}} (x-1) ((x-1) y(x)+1)}+1\right ) \log \left (\frac {2^{2/3} (-x y(x)+y(x)+2)}{\sqrt [3]{-\frac {1}{(x-1)^3}} (x-1) ((x-1) y(x)+1)}+2 (-2)^{2/3}\right )+3\right )}{9 \left (\frac {((x-1) y(x)-2)^3}{((x-1) y(x)+1)^3}+\frac {3 \sqrt [3]{-1} ((x-1) y(x)-2)}{\left (-\frac {1}{(x-1)^3}\right )^{4/3} (x-1)^4 ((x-1) y(x)+1)}+2\right )}=\frac {1}{9} 2^{2/3} \left (-\frac {1}{(x-1)^3}\right )^{2/3} (x-1)^2 (\log (1-x)-\log (x))+c_1,y(x)\right ]\] ✓ Maple : cpu = 1.955 (sec), leaf count = 32
\[y \relax (x ) = -\frac {2 \,{\mathrm e}^{-\LambertW \left (-\frac {2 \left (x -1\right ) {\mathrm e}^{3 c_{1}} {\mathrm e}^{-1}}{x}\right )+3 c_{1}-1}}{x}\]