\[ (y(x)+1) y'(x)-y(x)-x=0 \] ✓ Mathematica : cpu = 0.149561 (sec), leaf count = 71
\[\text {Solve}\left [\frac {1}{2} \log \left (\frac {x^2-y(x)^2+(x-3) y(x)-x-1}{(x-1)^2}\right )+\log (1-x)=c_1+\frac {\tanh ^{-1}\left (\frac {y(x)+2 x-1}{\sqrt {5} (y(x)+1)}\right )}{\sqrt {5}},y(x)\right ]\]
✓ Maple : cpu = 0.805 (sec), leaf count = 66
\[ \left \{ -{\frac {1}{2}\ln \left ( {\frac { \left ( y \left ( x \right ) \right ) ^{2}+ \left ( -x+3 \right ) y \left ( x \right ) -{x}^{2}+x+1}{ \left ( x-1 \right ) ^{2}}} \right ) }-{\frac {\sqrt {5}}{5}{\it Artanh} \left ( {\frac { \left ( -2\,y \left ( x \right ) -3+x \right ) \sqrt {5}}{5\,x-5}} \right ) }-\ln \left ( x-1 \right ) -{\it \_C1}=0 \right \} \]