\[ \boxed { \left ( 1+y \left ( x \right ) \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) -y \left ( x \right ) -x=0} \]
Mathematica: cpu = 0.100513 (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 = 0.624 (sec), leaf count = 73 \[ \left \{ -{\frac {1}{2}\ln \left ( -{\frac { \left ( x-1 \right ) ^{2}- \left ( x-1 \right ) \left ( -y \left ( x \right ) -1 \right ) - \left ( -y \left ( x \right ) -1 \right ) ^{2}}{ \left ( x-1 \right ) ^{2}}} \right ) }-{\frac {\sqrt {5}}{5}{\it Artanh} \left ( {\frac { \left ( x-3-2\,y \left ( x \right ) \right ) \sqrt {5}}{5\,x-5}} \right ) }-\ln \left ( x -1 \right ) -{\it \_C1}=0 \right \} \]