\[ y'(x)=\frac {(y(x)+1) (2 y(x)+1)}{x (2 x y(x)-2 y(x)+x-2)} \] ✓ Mathematica : cpu = 1.92831 (sec), leaf count = 149
\[\text {Solve}\left [\frac {2^{2/3} \left (x \log \left (-\frac {6\ 2^{2/3} (y(x)+1)}{2 (x-1) y(x)+x-2}\right )-x \log \left (\frac {3\ 2^{2/3} (2 x y(x)+x)}{2 (x-1) y(x)+x-2}\right )+2 x y(x) \left (\log \left (-\frac {6\ 2^{2/3} (y(x)+1)}{2 (x-1) y(x)+x-2}\right )-\log \left (\frac {3\ 2^{2/3} (2 x y(x)+x)}{2 (x-1) y(x)+x-2}\right )+\log (x)+1\right )+x+x \log (x)-1\right )}{9 (2 x y(x)+x)}=c_1,y(x)\right ]\] ✓ Maple : cpu = 0.13 (sec), leaf count = 45
\[y \relax (x ) = \frac {-x \LambertW \left (\frac {{\mathrm e}^{-\frac {1}{x}}}{x c_{1}}\right )-2}{2 x \LambertW \left (\frac {{\mathrm e}^{-\frac {1}{x}}}{x c_{1}}\right )+2}\]