\[ (y(x)+1) y'(x)-y(x)-x=0 \] ✓ Mathematica : cpu = 0.13845 (sec), leaf count = 71
\[\text {Solve}\left [\frac {1}{2} \log \left (\frac {x^2-y(x)^2+(x-3) y(x)-x-1}{(x-1)^2}\right )+\log (1-x)=\frac {\tanh ^{-1}\left (\frac {y(x)+2 x-1}{\sqrt {5} (y(x)+1)}\right )}{\sqrt {5}}+c_1,y(x)\right ]\] ✓ Maple : cpu = 0.789 (sec), leaf count = 66
\[-\frac {\ln \left (\frac {y \relax (x )^{2}+\left (-x +3\right ) y \relax (x )-x^{2}+x +1}{\left (x -1\right )^{2}}\right )}{2}-\frac {\sqrt {5}\, \arctanh \left (\frac {\left (-2 y \relax (x )-3+x \right ) \sqrt {5}}{5 x -5}\right )}{5}-\ln \left (x -1\right )-c_{1} = 0\]