\[ (y(x)+2 x-2) y'(x)-y(x)+x+1=0 \] ✓ Mathematica : cpu = 0.158436 (sec), leaf count = 80
\[\text {Solve}\left [6 \sqrt {3} \tan ^{-1}\left (\frac {4-3 y(x)}{\sqrt {3} (y(x)+2 x-2)}\right )=3 \log \left (\frac {3 x^2+3 y(x)^2+3 (x-3) y(x)-6 x+7}{(1-3 x)^2}\right )+6 \log (3 x-1)+2 c_1,y(x)\right ]\] ✓ Maple : cpu = 0.202 (sec), leaf count = 51
\[y \relax (x ) = \frac {3}{2}-\frac {x}{2}+\frac {\sqrt {3}\, \left (3 x -1\right ) \tan \left (\RootOf \left (\sqrt {3}\, \ln \left (\frac {3 \left (\tan ^{2}\left (\textit {\_Z} \right )+1\right ) \left (3 x -1\right )^{2}}{4}\right )+2 \sqrt {3}\, c_{1}+6 \textit {\_Z} \right )\right )}{6}\]