\[ \boxed { \left ( 2\,x \left ( y \left ( x \right ) \right ) ^{3}-{x}^{4} \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) - \left ( y \left ( x \right ) \right ) ^{4}+2\,{x}^{3}y \left ( x \right ) =0} \]
Mathematica: cpu = 0.114515 (sec), leaf count = 368 \[ \left \{\left \{y(x)\to \frac {\sqrt [3]{\frac {2}{3}} e^{c_1} x}{\sqrt [3]{\sqrt {3} \sqrt {27 x^6-4 e^{3 c_1} x^3}-9 x^3}}+\frac {\sqrt [3]{\sqrt {3} \sqrt {27 x^6-4 e^{3 c_1} x^3}-9 x^3}}{\sqrt [3]{2} 3^{2/3}}\right \},\left \{y(x)\to -\frac {\left (1+i \sqrt {3}\right ) e^{c_1} x}{2^{2/3} \sqrt [3]{3} \sqrt [3]{\sqrt {3} \sqrt {27 x^6-4 e^{3 c_1} x^3}-9 x^3}}-\frac {\left (1-i \sqrt {3}\right ) \sqrt [3]{\sqrt {3} \sqrt {27 x^6-4 e^{3 c_1} x^3}-9 x^3}}{2 \sqrt [3]{2} 3^{2/3}}\right \},\left \{y(x)\to -\frac {\left (1-i \sqrt {3}\right ) e^{c_1} x}{2^{2/3} \sqrt [3]{3} \sqrt [3]{\sqrt {3} \sqrt {27 x^6-4 e^{3 c_1} x^3}-9 x^3}}-\frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{\sqrt {3} \sqrt {27 x^6-4 e^{3 c_1} x^3}-9 x^3}}{2 \sqrt [3]{2} 3^{2/3}}\right \}\right \} \]
Maple: cpu = 0.062 (sec), leaf count = 447 \[ \left \{ y \left ( x \right ) ={\frac {\sqrt [3]{12}}{6\,{\it \_C1}} \sqrt [3]{x \left ( -9\,{x}^{2}{\it \_C1}+\sqrt {3}\sqrt {{\frac {x \left ( 27\,{x}^{3}{{\it \_C1}}^{3}-4 \right ) }{{\it \_C1}}}} \right ) {{\it \_C1}}^{2}}}+{\frac {x{12}^{{\frac {2}{3}}}}{6}{\frac {1}{\sqrt [3]{x \left ( -9\,{x}^{2}{\it \_C1}+\sqrt {3}\sqrt {{\frac {x \left ( 27 \,{x}^{3}{{\it \_C1}}^{3}-4 \right ) }{{\it \_C1}}}} \right ) {{\it \_C1 }}^{2}}}}},y \left ( x \right ) =-{\frac {\sqrt [3]{12}}{12\,{\it \_C1}} \sqrt [3]{x \left ( -9\,{x}^{2}{\it \_C1}+\sqrt {3}\sqrt {{\frac {x \left ( 27\,{x}^{3}{{\it \_C1}}^{3}-4 \right ) }{{\it \_C1}}}} \right ) {{\it \_C1}}^{2}}}-{\frac {x{12}^{{\frac {2}{3}}}}{12}{\frac {1}{ \sqrt [3]{x \left ( -9\,{x}^{2}{\it \_C1}+\sqrt {3}\sqrt {{\frac {x \left ( 27\,{x}^{3}{{\it \_C1}}^{3}-4 \right ) }{{\it \_C1}}}} \right ) {{\it \_C1}}^{2}}}}}-{\frac {i}{2}}\sqrt {3} \left ( {\frac {\sqrt [3]{ 12}}{6\,{\it \_C1}}\sqrt [3]{x \left ( -9\,{x}^{2}{\it \_C1}+\sqrt {3} \sqrt {{\frac {x \left ( 27\,{x}^{3}{{\it \_C1}}^{3}-4 \right ) }{{\it \_C1}}}} \right ) {{\it \_C1}}^{2}}}-{\frac {x{12}^{{\frac {2}{3}}}}{6} {\frac {1}{\sqrt [3]{x \left ( -9\,{x}^{2}{\it \_C1}+\sqrt {3}\sqrt {{ \frac {x \left ( 27\,{x}^{3}{{\it \_C1}}^{3}-4 \right ) }{{\it \_C1}}}} \right ) {{\it \_C1}}^{2}}}}} \right ) ,y \left ( x \right ) =-{\frac { \sqrt [3]{12}}{12\,{\it \_C1}}\sqrt [3]{x \left ( -9\,{x}^{2}{\it \_C1} +\sqrt {3}\sqrt {{\frac {x \left ( 27\,{x}^{3}{{\it \_C1}}^{3}-4 \right ) }{{\it \_C1}}}} \right ) {{\it \_C1}}^{2}}}-{\frac {x{12}^{{ \frac {2}{3}}}}{12}{\frac {1}{\sqrt [3]{x \left ( -9\,{x}^{2}{\it \_C1} +\sqrt {3}\sqrt {{\frac {x \left ( 27\,{x}^{3}{{\it \_C1}}^{3}-4 \right ) }{{\it \_C1}}}} \right ) {{\it \_C1}}^{2}}}}}+{\frac {i}{2}} \sqrt {3} \left ( {\frac {\sqrt [3]{12}}{6\,{\it \_C1}}\sqrt [3]{x \left ( -9\,{x}^{2}{\it \_C1}+\sqrt {3}\sqrt {{\frac {x \left ( 27\,{x} ^{3}{{\it \_C1}}^{3}-4 \right ) }{{\it \_C1}}}} \right ) {{\it \_C1}}^{2 }}}-{\frac {x{12}^{{\frac {2}{3}}}}{6}{\frac {1}{\sqrt [3]{x \left ( -9 \,{x}^{2}{\it \_C1}+\sqrt {3}\sqrt {{\frac {x \left ( 27\,{x}^{3}{{\it \_C1}}^{3}-4 \right ) }{{\it \_C1}}}} \right ) {{\it \_C1}}^{2}}}}} \right ) \right \} \]