\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac { \left ( x+y \left ( x \right ) +1 \right ) y \left ( x \right ) }{ \left ( 2\, \left ( y \left ( x \right ) \right ) ^{3}+y \left ( x \right ) +x \right ) \left ( 1+x \right ) }}=0} \]
Mathematica: cpu = 0.552070 (sec), leaf count = 27 \[ \text {Solve}\left [y(x)^2-\frac {x}{y(x)}+\log (y(x))-\log (x+1)=c_1,y(x)\right ] \]
Maple: cpu = 0.109 (sec), leaf count = 30 \[ \left \{ y \left ( x \right ) ={{\rm e}^{{\it RootOf} \left ( - \left ( { {\rm e}^{{\it \_Z}}} \right ) ^{3}+\ln \left ( 1+x \right ) {{\rm e}^{{ \it \_Z}}}+{\it \_C1}\,{{\rm e}^{{\it \_Z}}}-{\it \_Z}\,{{\rm e}^{{ \it \_Z}}}+x \right ) }} \right \} \]