\[ (y(x)+1) y'(x)-y(x)-x=0 \] ✓ Mathematica : cpu = 0.14623 (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 = 0.823 (sec), leaf count = 66
\[\left \{-c_{1}-\frac {\sqrt {5}\, \arctanh \left (\frac {\left (x -2 y \left (x \right )-3\right ) \sqrt {5}}{5 x -5}\right )}{5}-\frac {\ln \left (\frac {-x^{2}+y \left (x \right )^{2}+x +\left (-x +3\right ) y \left (x \right )+1}{\left (x -1\right )^{2}}\right )}{2}-\ln \left (x -1\right ) = 0\right \}\]