\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {y \left ( x \right ) \left ( -1+\ln \left ( x \left ( 1+x \right ) \right ) y \left ( x \right ) {x}^{4}-\ln \left ( x \left ( 1+x \right ) \right ) {x}^{3} \right ) }{x}}=0} \]
Mathematica: cpu = 0.361046 (sec), leaf count = 84 \[ \left \{\left \{y(x)\to \frac {e^{\frac {2 x^3}{9}+\frac {x}{3}}}{c_1 e^{\frac {x^2}{6}} x \sqrt [3]{x+1} (x (x+1))^{\frac {x^3}{3}}+e^{\frac {x^2}{6}+\frac {1}{18} \left (4 x^2-3 x+6\right ) x} x}\right \}\right \} \]
Maple: cpu = 0.109 (sec), leaf count = 166 \[ \left \{ y \left ( x \right ) ={\frac {1}{x} \left ( x \left ( 1+x \right ) \right ) ^{-{\frac {{x}^{3}}{3}}}{{\rm e}^{{\frac {2\,{x}^{3} }{9}}}}{{\rm e}^{-{\frac {{x}^{2}}{6}}}}{{\rm e}^{{\frac {x}{3}}}} \left ( {x}^{-{\frac {{x}^{3}}{3}}} \left ( 1+x \right ) ^{-{\frac {{x}^ {3}}{3}}}{{\rm e}^{{\frac {x \left ( 3\,i{x}^{2} \left ( {\it csgn} \left ( ix \left ( 1+x \right ) \right ) \right ) ^{3}\pi -3\,i{x}^{2} \left ( {\it csgn} \left ( ix \left ( 1+x \right ) \right ) \right ) ^{2} {\it csgn} \left ( ix \right ) \pi -3\,i{x}^{2} \left ( {\it csgn} \left ( ix \left ( 1+x \right ) \right ) \right ) ^{2}{\it csgn} \left ( i \left ( 1+x \right ) \right ) \pi +3\,i{x}^{2}{\it csgn} \left ( ix \left ( 1+x \right ) \right ) {\it csgn} \left ( ix \right ) {\it csgn} \left ( i \left ( 1+x \right ) \right ) \pi +4\,{x}^{2}-3\,x+6 \right ) }{18}}}}+{\it \_C1}\,\sqrt [3]{1+x} \right ) ^{-1}} \right \} \]