2.324   ODE No. 324

$\left (2 x^3 y(x)^3-x\right ) y'(x)+2 x^3 y(x)^3-y(x)=0$ Mathematica : cpu = 0.115438 (sec), leaf count = 723

$\left \{\left \{y(x)\to \frac {\left (2 x^3-c_1 x^2\right ){}^2}{6 x^2 \sqrt [3]{-8 x^9-27 x^4+12 c_1 x^8-6 c_1{}^2 x^7+c_1{}^3 x^6+3 \sqrt {3} \sqrt {16 x^{13}+27 x^8-24 c_1 x^{12}+12 c_1{}^2 x^{11}-2 c_1{}^3 x^{10}}}}-\frac {2 x^3-c_1 x^2}{6 x^2}+\frac {\sqrt [3]{-8 x^9-27 x^4+12 c_1 x^8-6 c_1{}^2 x^7+c_1{}^3 x^6+3 \sqrt {3} \sqrt {16 x^{13}+27 x^8-24 c_1 x^{12}+12 c_1{}^2 x^{11}-2 c_1{}^3 x^{10}}}}{6 x^2}\right \},\left \{y(x)\to -\frac {\left (1+i \sqrt {3}\right ) \left (2 x^3-c_1 x^2\right ){}^2}{12 x^2 \sqrt [3]{-8 x^9-27 x^4+12 c_1 x^8-6 c_1{}^2 x^7+c_1{}^3 x^6+3 \sqrt {3} \sqrt {16 x^{13}+27 x^8-24 c_1 x^{12}+12 c_1{}^2 x^{11}-2 c_1{}^3 x^{10}}}}-\frac {2 x^3-c_1 x^2}{6 x^2}-\frac {\left (1-i \sqrt {3}\right ) \sqrt [3]{-8 x^9-27 x^4+12 c_1 x^8-6 c_1{}^2 x^7+c_1{}^3 x^6+3 \sqrt {3} \sqrt {16 x^{13}+27 x^8-24 c_1 x^{12}+12 c_1{}^2 x^{11}-2 c_1{}^3 x^{10}}}}{12 x^2}\right \},\left \{y(x)\to -\frac {\left (1-i \sqrt {3}\right ) \left (2 x^3-c_1 x^2\right ){}^2}{12 x^2 \sqrt [3]{-8 x^9-27 x^4+12 c_1 x^8-6 c_1{}^2 x^7+c_1{}^3 x^6+3 \sqrt {3} \sqrt {16 x^{13}+27 x^8-24 c_1 x^{12}+12 c_1{}^2 x^{11}-2 c_1{}^3 x^{10}}}}-\frac {2 x^3-c_1 x^2}{6 x^2}-\frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{-8 x^9-27 x^4+12 c_1 x^8-6 c_1{}^2 x^7+c_1{}^3 x^6+3 \sqrt {3} \sqrt {16 x^{13}+27 x^8-24 c_1 x^{12}+12 c_1{}^2 x^{11}-2 c_1{}^3 x^{10}}}}{12 x^2}\right \}\right \}$ Maple : cpu = 0.097 (sec), leaf count = 815

$\left \{ y \left ( x \right ) ={\frac {1}{12\,x} \left ( \left ( 2\,{\it \_C1}\,x-4\,{x}^{2} \right ) \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}+ \left ( -4\,i{x}^{4}+4\,i{\it \_C1}\,{x}^{3}-i{{\it \_C1}}^{2}{x}^{2}+i \left ( \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 ) ^{{\frac {2}{3}}} \right ) \sqrt {3}-4\,{x}^{4}+4\,{\it \_C1}\,{x}^{3}-{{\it \_C1}}^{2}{x}^{2}- \left ( \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 ) ^{{\frac {2}{3}}} \right ) {\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}}}},y \left ( x \right ) =-{\frac {1}{12\,x} \left ( \left ( -2\,{\it \_C1}\,x+4\,{x}^{2} \right ) \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}+ \left ( -4\,i{x}^{4}+4\,i{\it \_C1}\,{x}^{3}-i{{\it \_C1}}^{2}{x}^{2}+i \left ( \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 ) ^{{\frac {2}{3}}} \right ) \sqrt {3}+4\,{x}^{4}-4\,{\it \_C1}\,{x}^{3}+{{\it \_C1}}^{2}{x}^{2}+ \left ( \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 ) ^{{\frac {2}{3}}} \right ) {\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}}}},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}} \right \}$