\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {y \left ( x \right ) \left ( y \left ( x \right ) +x \right ) }{x \left ( x+ \left ( y \left ( x \right ) \right ) ^{3} \right ) }}=0} \]
Mathematica: cpu = 0.382549 (sec), leaf count = 285 \[ \left \{\left \{y(x)\to \frac {2 \sqrt [3]{2} \left (c_1+\log (x)\right )}{\sqrt [3]{\sqrt {2916 x^2-864 \left (c_1+\log (x)\right ){}^3}+54 x}}+\frac {\sqrt [3]{\sqrt {2916 x^2-864 \left (c_1+\log (x)\right ){}^3}+54 x}}{3 \sqrt [3]{2}}\right \},\left \{y(x)\to -\frac {\sqrt [3]{2} \left (1+i \sqrt {3}\right ) \left (c_1+\log (x)\right )}{\sqrt [3]{\sqrt {2916 x^2-864 \left (c_1+\log (x)\right ){}^3}+54 x}}-\frac {\left (1-i \sqrt {3}\right ) \sqrt [3]{\sqrt {2916 x^2-864 \left (c_1+\log (x)\right ){}^3}+54 x}}{6 \sqrt [3]{2}}\right \},\left \{y(x)\to -\frac {\sqrt [3]{2} \left (1-i \sqrt {3}\right ) \left (c_1+\log (x)\right )}{\sqrt [3]{\sqrt {2916 x^2-864 \left (c_1+\log (x)\right ){}^3}+54 x}}-\frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{\sqrt {2916 x^2-864 \left (c_1+\log (x)\right ){}^3}+54 x}}{6 \sqrt [3]{2}}\right \}\right \} \]
Maple: cpu = 0.078 (sec), leaf count = 497 \[ \left \{ y \left ( x \right ) ={\frac {1}{3}\sqrt [3]{27\,x+3\,\sqrt {- 24\,{{\it \_C1}}^{3}-72\,\ln \left ( x \right ) {{\it \_C1}}^{2}-72\, \left ( \ln \left ( x \right ) \right ) ^{2}{\it \_C1}-24\, \left ( \ln \left ( x \right ) \right ) ^{3}+81\,{x}^{2}}}}-3\,{\frac {-2/3\,{\it \_C1}-2/3\,\ln \left ( x \right ) }{\sqrt [3]{27\,x+3\,\sqrt {-24\,{{ \it \_C1}}^{3}-72\,\ln \left ( x \right ) {{\it \_C1}}^{2}-72\, \left ( \ln \left ( x \right ) \right ) ^{2}{\it \_C1}-24\, \left ( \ln \left ( x \right ) \right ) ^{3}+81\,{x}^{2}}}}},y \left ( x \right ) =-{\frac {1 }{6}\sqrt [3]{27\,x+3\,\sqrt {-24\,{{\it \_C1}}^{3}-72\,\ln \left ( x \right ) {{\it \_C1}}^{2}-72\, \left ( \ln \left ( x \right ) \right ) ^ {2}{\it \_C1}-24\, \left ( \ln \left ( x \right ) \right ) ^{3}+81\,{x}^ {2}}}}+{\frac {3}{2} \left ( -{\frac {2\,{\it \_C1}}{3}}-{\frac {2\, \ln \left ( x \right ) }{3}} \right ) {\frac {1}{\sqrt [3]{27\,x+3\, \sqrt {-24\,{{\it \_C1}}^{3}-72\,\ln \left ( x \right ) {{\it \_C1}}^{2 }-72\, \left ( \ln \left ( x \right ) \right ) ^{2}{\it \_C1}-24\, \left ( \ln \left ( x \right ) \right ) ^{3}+81\,{x}^{2}}}}}}-{\frac {i }{2}}\sqrt {3} \left ( {\frac {1}{3}\sqrt [3]{27\,x+3\,\sqrt {-24\,{{ \it \_C1}}^{3}-72\,\ln \left ( x \right ) {{\it \_C1}}^{2}-72\, \left ( \ln \left ( x \right ) \right ) ^{2}{\it \_C1}-24\, \left ( \ln \left ( x \right ) \right ) ^{3}+81\,{x}^{2}}}}+3\,{\frac {-2/3\,{\it \_C1}-2/3 \,\ln \left ( x \right ) }{\sqrt [3]{27\,x+3\,\sqrt {-24\,{{\it \_C1}}^ {3}-72\,\ln \left ( x \right ) {{\it \_C1}}^{2}-72\, \left ( \ln \left ( x \right ) \right ) ^{2}{\it \_C1}-24\, \left ( \ln \left ( x \right ) \right ) ^{3}+81\,{x}^{2}}}}} \right ) ,y \left ( x \right ) =-{ \frac {1}{6}\sqrt [3]{27\,x+3\,\sqrt {-24\,{{\it \_C1}}^{3}-72\,\ln \left ( x \right ) {{\it \_C1}}^{2}-72\, \left ( \ln \left ( x \right ) \right ) ^{2}{\it \_C1}-24\, \left ( \ln \left ( x \right ) \right ) ^{3 }+81\,{x}^{2}}}}+{\frac {3}{2} \left ( -{\frac {2\,{\it \_C1}}{3}}-{ \frac {2\,\ln \left ( x \right ) }{3}} \right ) {\frac {1}{\sqrt [3]{27 \,x+3\,\sqrt {-24\,{{\it \_C1}}^{3}-72\,\ln \left ( x \right ) {{\it \_C1}}^{2}-72\, \left ( \ln \left ( x \right ) \right ) ^{2}{\it \_C1}- 24\, \left ( \ln \left ( x \right ) \right ) ^{3}+81\,{x}^{2}}}}}}+{ \frac {i}{2}}\sqrt {3} \left ( {\frac {1}{3}\sqrt [3]{27\,x+3\,\sqrt {- 24\,{{\it \_C1}}^{3}-72\,\ln \left ( x \right ) {{\it \_C1}}^{2}-72\, \left ( \ln \left ( x \right ) \right ) ^{2}{\it \_C1}-24\, \left ( \ln \left ( x \right ) \right ) ^{3}+81\,{x}^{2}}}}+3\,{\frac {-2/3\,{\it \_C1}-2/3\,\ln \left ( x \right ) }{\sqrt [3]{27\,x+3\,\sqrt {-24\,{{ \it \_C1}}^{3}-72\,\ln \left ( x \right ) {{\it \_C1}}^{2}-72\, \left ( \ln \left ( x \right ) \right ) ^{2}{\it \_C1}-24\, \left ( \ln \left ( x \right ) \right ) ^{3}+81\,{x}^{2}}}}} \right ) \right \} \]