\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac { \left ( \ln \left ( y \left ( x \right ) \right ) x+\ln \left ( y \left ( x \right ) \right ) +x \right ) y \left ( x \right ) }{x \left ( 1+x \right ) }}=0} \]
Mathematica: cpu = 0.063508 (sec), leaf count = 22 \[ \left \{\left \{y(x)\to x^x (x+1)^{-x} e^{c_1 x}\right \}\right \} \]
Maple: cpu = 0.093 (sec), leaf count = 14 \[ \left \{ y \left ( x \right ) = \left ( {\frac {{\it \_C1}\,x}{1+x}} \right ) ^{x} \right \} \]