\[ \boxed { \left ( 2\,{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}-x \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +2\,{x}^{3} \left ( y \left ( x \right ) \right ) ^{3}-y \left ( x \right ) =0} \]
Mathematica: cpu = 0.026003 (sec), leaf count = 723 \[ \left \{\left \{y(x)\to -\frac {2 x^3-c_1 x^2}{6 x^2}+\frac {\sqrt [3]{12 c_1 x^8-6 c_1^2 x^7+c_1^3 x^6+3 \sqrt {3} \sqrt {-24 c_1 x^{12}+12 c_1^2 x^{11}-2 c_1^3 x^{10}+16 x^{13}+27 x^8}-8 x^9-27 x^4}}{6 x^2}+\frac {\left (2 x^3-c_1 x^2\right ){}^2}{6 x^2 \sqrt [3]{12 c_1 x^8-6 c_1^2 x^7+c_1^3 x^6+3 \sqrt {3} \sqrt {-24 c_1 x^{12}+12 c_1^2 x^{11}-2 c_1^3 x^{10}+16 x^{13}+27 x^8}-8 x^9-27 x^4}}\right \},\left \{y(x)\to -\frac {2 x^3-c_1 x^2}{6 x^2}-\frac {\left (1-i \sqrt {3}\right ) \sqrt [3]{12 c_1 x^8-6 c_1^2 x^7+c_1^3 x^6+3 \sqrt {3} \sqrt {-24 c_1 x^{12}+12 c_1^2 x^{11}-2 c_1^3 x^{10}+16 x^{13}+27 x^8}-8 x^9-27 x^4}}{12 x^2}-\frac {\left (1+i \sqrt {3}\right ) \left (2 x^3-c_1 x^2\right ){}^2}{12 x^2 \sqrt [3]{12 c_1 x^8-6 c_1^2 x^7+c_1^3 x^6+3 \sqrt {3} \sqrt {-24 c_1 x^{12}+12 c_1^2 x^{11}-2 c_1^3 x^{10}+16 x^{13}+27 x^8}-8 x^9-27 x^4}}\right \},\left \{y(x)\to -\frac {2 x^3-c_1 x^2}{6 x^2}-\frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{12 c_1 x^8-6 c_1^2 x^7+c_1^3 x^6+3 \sqrt {3} \sqrt {-24 c_1 x^{12}+12 c_1^2 x^{11}-2 c_1^3 x^{10}+16 x^{13}+27 x^8}-8 x^9-27 x^4}}{12 x^2}-\frac {\left (1-i \sqrt {3}\right ) \left (2 x^3-c_1 x^2\right ){}^2}{12 x^2 \sqrt [3]{12 c_1 x^8-6 c_1^2 x^7+c_1^3 x^6+3 \sqrt {3} \sqrt {-24 c_1 x^{12}+12 c_1^2 x^{11}-2 c_1^3 x^{10}+16 x^{13}+27 x^8}-8 x^9-27 x^4}}\right \}\right \} \]
Maple: cpu = 0.109 (sec), leaf count = 770 \[ \left \{ y \left ( x \right ) ={\frac {1}{6\,x}\sqrt [3]{ \left ( {{\it \_C1}}^{3}{x}^{2}-6\,{{\it \_C1}}^{2}{x}^{3}+12\,{\it \_C1}\,{x}^{4}-8 \,{x}^{5}+3\,\sqrt {-6\,{{\it \_C1}}^{3}{x}^{2}+36\,{{\it \_C1}}^{2}{x }^{3}-72\,{\it \_C1}\,{x}^{4}+48\,{x}^{5}+81}-27 \right ) x}}+{\frac { \left ( {\it \_C1}-2\,x \right ) ^{2}x}{6}{\frac {1}{\sqrt [3]{ \left ( {{\it \_C1}}^{3}{x}^{2}-6\,{{\it \_C1}}^{2}{x}^{3}+12\,{\it \_C1}\,{x} ^{4}-8\,{x}^{5}+3\,\sqrt {-6\,{{\it \_C1}}^{3}{x}^{2}+36\,{{\it \_C1}} ^{2}{x}^{3}-72\,{\it \_C1}\,{x}^{4}+48\,{x}^{5}+81}-27 \right ) x}}}}+{ \frac {{\it \_C1}}{6}}-{\frac {x}{3}},y \left ( x \right ) =-{\frac {1}{ 12\,x}\sqrt [3]{ \left ( {{\it \_C1}}^{3}{x}^{2}-6\,{{\it \_C1}}^{2}{x} ^{3}+12\,{\it \_C1}\,{x}^{4}-8\,{x}^{5}+3\,\sqrt {-6\,{{\it \_C1}}^{3} {x}^{2}+36\,{{\it \_C1}}^{2}{x}^{3}-72\,{\it \_C1}\,{x}^{4}+48\,{x}^{5 }+81}-27 \right ) x}}-{\frac { \left ( {\it \_C1}-2\,x \right ) ^{2}x}{12 }{\frac {1}{\sqrt [3]{ \left ( {{\it \_C1}}^{3}{x}^{2}-6\,{{\it \_C1}}^ {2}{x}^{3}+12\,{\it \_C1}\,{x}^{4}-8\,{x}^{5}+3\,\sqrt {-6\,{{\it \_C1 }}^{3}{x}^{2}+36\,{{\it \_C1}}^{2}{x}^{3}-72\,{\it \_C1}\,{x}^{4}+48\, {x}^{5}+81}-27 \right ) x}}}}+{\frac {{\it \_C1}}{6}}-{\frac {x}{3}}-{ \frac {i}{2}}\sqrt {3} \left ( {\frac {1}{6\,x}\sqrt [3]{ \left ( {{\it \_C1}}^{3}{x}^{2}-6\,{{\it \_C1}}^{2}{x}^{3}+12\,{\it \_C1}\,{x}^{4}-8 \,{x}^{5}+3\,\sqrt {-6\,{{\it \_C1}}^{3}{x}^{2}+36\,{{\it \_C1}}^{2}{x }^{3}-72\,{\it \_C1}\,{x}^{4}+48\,{x}^{5}+81}-27 \right ) x}}-{\frac { \left ( {\it \_C1}-2\,x \right ) ^{2}x}{6}{\frac {1}{\sqrt [3]{ \left ( {{\it \_C1}}^{3}{x}^{2}-6\,{{\it \_C1}}^{2}{x}^{3}+12\,{\it \_C1}\,{x} ^{4}-8\,{x}^{5}+3\,\sqrt {-6\,{{\it \_C1}}^{3}{x}^{2}+36\,{{\it \_C1}} ^{2}{x}^{3}-72\,{\it \_C1}\,{x}^{4}+48\,{x}^{5}+81}-27 \right ) x}}}} \right ) ,y \left ( x \right ) =-{\frac {1}{12\,x}\sqrt [3]{ \left ( {{ \it \_C1}}^{3}{x}^{2}-6\,{{\it \_C1}}^{2}{x}^{3}+12\,{\it \_C1}\,{x}^{ 4}-8\,{x}^{5}+3\,\sqrt {-6\,{{\it \_C1}}^{3}{x}^{2}+36\,{{\it \_C1}}^{ 2}{x}^{3}-72\,{\it \_C1}\,{x}^{4}+48\,{x}^{5}+81}-27 \right ) x}}-{ \frac { \left ( {\it \_C1}-2\,x \right ) ^{2}x}{12}{\frac {1}{\sqrt [3]{ \left ( {{\it \_C1}}^{3}{x}^{2}-6\,{{\it \_C1}}^{2}{x}^{3}+12\,{\it \_C1}\,{x}^{4}-8\,{x}^{5}+3\,\sqrt {-6\,{{\it \_C1}}^{3}{x}^{2}+36\,{{ \it \_C1}}^{2}{x}^{3}-72\,{\it \_C1}\,{x}^{4}+48\,{x}^{5}+81}-27 \right ) x}}}}+{\frac {{\it \_C1}}{6}}-{\frac {x}{3}}+{\frac {i}{2}} \sqrt {3} \left ( {\frac {1}{6\,x}\sqrt [3]{ \left ( {{\it \_C1}}^{3}{x} ^{2}-6\,{{\it \_C1}}^{2}{x}^{3}+12\,{\it \_C1}\,{x}^{4}-8\,{x}^{5}+3\, \sqrt {-6\,{{\it \_C1}}^{3}{x}^{2}+36\,{{\it \_C1}}^{2}{x}^{3}-72\,{ \it \_C1}\,{x}^{4}+48\,{x}^{5}+81}-27 \right ) x}}-{\frac { \left ( { \it \_C1}-2\,x \right ) ^{2}x}{6}{\frac {1}{\sqrt [3]{ \left ( {{\it \_C1}}^{3}{x}^{2}-6\,{{\it \_C1}}^{2}{x}^{3}+12\,{\it \_C1}\,{x}^{4}-8 \,{x}^{5}+3\,\sqrt {-6\,{{\it \_C1}}^{3}{x}^{2}+36\,{{\it \_C1}}^{2}{x }^{3}-72\,{\it \_C1}\,{x}^{4}+48\,{x}^{5}+81}-27 \right ) x}}}} \right ) \right \} \]