\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {y \left ( x \right ) \left ( x-y \left ( x \right ) \right ) }{x \left ( x- \left ( y \left ( x \right ) \right ) ^{3} \right ) }}=0} \]
Mathematica: cpu = 0.355045 (sec), leaf count = 327 \[ \left \{\left \{y(x)\to \frac {\sqrt [3]{2} \left (6 c_1-6 \log (x)\right )}{3 \sqrt [3]{\sqrt {4 \left (6 c_1-6 \log (x)\right ){}^3+2916 x^2}+54 x}}-\frac {\sqrt [3]{\sqrt {4 \left (6 c_1-6 \log (x)\right ){}^3+2916 x^2}+54 x}}{3 \sqrt [3]{2}}\right \},\left \{y(x)\to \frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{\sqrt {4 \left (6 c_1-6 \log (x)\right ){}^3+2916 x^2}+54 x}}{6 \sqrt [3]{2}}-\frac {\left (1-i \sqrt {3}\right ) \left (6 c_1-6 \log (x)\right )}{3\ 2^{2/3} \sqrt [3]{\sqrt {4 \left (6 c_1-6 \log (x)\right ){}^3+2916 x^2}+54 x}}\right \},\left \{y(x)\to \frac {\left (1-i \sqrt {3}\right ) \sqrt [3]{\sqrt {4 \left (6 c_1-6 \log (x)\right ){}^3+2916 x^2}+54 x}}{6 \sqrt [3]{2}}-\frac {\left (1+i \sqrt {3}\right ) \left (6 c_1-6 \log (x)\right )}{3\ 2^{2/3} \sqrt [3]{\sqrt {4 \left (6 c_1-6 \log (x)\right ){}^3+2916 x^2}+54 x}}\right \}\right \} \]
Maple: cpu = 0.093 (sec), leaf count = 497 \[ \left \{ y \left ( x \right ) ={\frac {1}{3}\sqrt [3]{-27\,x+3\,\sqrt {- 24\, \left ( \ln \left ( x \right ) \right ) ^{3}+72\, \left ( \ln \left ( x \right ) \right ) ^{2}{\it \_C1}-72\,\ln \left ( x \right ) {{ \it \_C1}}^{2}+24\,{{\it \_C1}}^{3}+81\,{x}^{2}}}}-3\,{\frac {-2/3\, \ln \left ( x \right ) +2/3\,{\it \_C1}}{\sqrt [3]{-27\,x+3\,\sqrt {-24 \, \left ( \ln \left ( x \right ) \right ) ^{3}+72\, \left ( \ln \left ( x \right ) \right ) ^{2}{\it \_C1}-72\,\ln \left ( x \right ) {{\it \_C1 }}^{2}+24\,{{\it \_C1}}^{3}+81\,{x}^{2}}}}},y \left ( x \right ) =-{ \frac {1}{6}\sqrt [3]{-27\,x+3\,\sqrt {-24\, \left ( \ln \left ( x \right ) \right ) ^{3}+72\, \left ( \ln \left ( x \right ) \right ) ^{2} {\it \_C1}-72\,\ln \left ( x \right ) {{\it \_C1}}^{2}+24\,{{\it \_C1}} ^{3}+81\,{x}^{2}}}}+{\frac {3}{2} \left ( -{\frac {2\,\ln \left ( x \right ) }{3}}+{\frac {2\,{\it \_C1}}{3}} \right ) {\frac {1}{\sqrt [3] {-27\,x+3\,\sqrt {-24\, \left ( \ln \left ( x \right ) \right ) ^{3}+72 \, \left ( \ln \left ( x \right ) \right ) ^{2}{\it \_C1}-72\,\ln \left ( x \right ) {{\it \_C1}}^{2}+24\,{{\it \_C1}}^{3}+81\,{x}^{2}}}} }}-{\frac {i}{2}}\sqrt {3} \left ( {\frac {1}{3}\sqrt [3]{-27\,x+3\, \sqrt {-24\, \left ( \ln \left ( x \right ) \right ) ^{3}+72\, \left ( \ln \left ( x \right ) \right ) ^{2}{\it \_C1}-72\,\ln \left ( x \right ) {{\it \_C1}}^{2}+24\,{{\it \_C1}}^{3}+81\,{x}^{2}}}}+3\,{ \frac {-2/3\,\ln \left ( x \right ) +2/3\,{\it \_C1}}{\sqrt [3]{-27\,x+ 3\,\sqrt {-24\, \left ( \ln \left ( x \right ) \right ) ^{3}+72\, \left ( \ln \left ( x \right ) \right ) ^{2}{\it \_C1}-72\,\ln \left ( x \right ) {{\it \_C1}}^{2}+24\,{{\it \_C1}}^{3}+81\,{x}^{2}}}}} \right ) ,y \left ( x \right ) =-{\frac {1}{6}\sqrt [3]{-27\,x+3\,\sqrt {-24\, \left ( \ln \left ( x \right ) \right ) ^{3}+72\, \left ( \ln \left ( x \right ) \right ) ^{2}{\it \_C1}-72\,\ln \left ( x \right ) {{ \it \_C1}}^{2}+24\,{{\it \_C1}}^{3}+81\,{x}^{2}}}}+{\frac {3}{2} \left ( -{\frac {2\,\ln \left ( x \right ) }{3}}+{\frac {2\,{\it \_C1} }{3}} \right ) {\frac {1}{\sqrt [3]{-27\,x+3\,\sqrt {-24\, \left ( \ln \left ( x \right ) \right ) ^{3}+72\, \left ( \ln \left ( x \right ) \right ) ^{2}{\it \_C1}-72\,\ln \left ( x \right ) {{\it \_C1}}^{2}+24 \,{{\it \_C1}}^{3}+81\,{x}^{2}}}}}}+{\frac {i}{2}}\sqrt {3} \left ( { \frac {1}{3}\sqrt [3]{-27\,x+3\,\sqrt {-24\, \left ( \ln \left ( x \right ) \right ) ^{3}+72\, \left ( \ln \left ( x \right ) \right ) ^{2} {\it \_C1}-72\,\ln \left ( x \right ) {{\it \_C1}}^{2}+24\,{{\it \_C1}} ^{3}+81\,{x}^{2}}}}+3\,{\frac {-2/3\,\ln \left ( x \right ) +2/3\,{\it \_C1}}{\sqrt [3]{-27\,x+3\,\sqrt {-24\, \left ( \ln \left ( x \right ) \right ) ^{3}+72\, \left ( \ln \left ( x \right ) \right ) ^{2}{\it \_C1 }-72\,\ln \left ( x \right ) {{\it \_C1}}^{2}+24\,{{\it \_C1}}^{3}+81\, {x}^{2}}}}} \right ) \right \} \]