\[ y'(x)=\frac {2 y(x)^6}{32 x^2 y(x)^4+y(x)^3+16 x y(x)^2+2} \] ✓ Mathematica : cpu = 0.123024 (sec), leaf count = 705
\[\left \{\left \{y(x)\to \frac {\sqrt [3]{18432 c_1^2 x^2+\sqrt {4 \left (192 c_1^2 x-12 c_1-256 x^2\right ){}^3+\left (18432 c_1^2 x^2-2880 c_1 x+8192 x^3+108\right ){}^2}-2880 c_1 x+8192 x^3+108}}{3 \sqrt [3]{2} \left (1-16 c_1 x\right )}-\frac {\sqrt [3]{2} \left (192 c_1^2 x-12 c_1-256 x^2\right )}{3 \left (1-16 c_1 x\right ) \sqrt [3]{18432 c_1^2 x^2+\sqrt {4 \left (192 c_1^2 x-12 c_1-256 x^2\right ){}^3+\left (18432 c_1^2 x^2-2880 c_1 x+8192 x^3+108\right ){}^2}-2880 c_1 x+8192 x^3+108}}+\frac {16 x}{3 \left (1-16 c_1 x\right )}\right \},\left \{y(x)\to -\frac {\left (1-i \sqrt {3}\right ) \sqrt [3]{18432 c_1^2 x^2+\sqrt {4 \left (192 c_1^2 x-12 c_1-256 x^2\right ){}^3+\left (18432 c_1^2 x^2-2880 c_1 x+8192 x^3+108\right ){}^2}-2880 c_1 x+8192 x^3+108}}{6 \sqrt [3]{2} \left (1-16 c_1 x\right )}+\frac {\left (1+i \sqrt {3}\right ) \left (192 c_1^2 x-12 c_1-256 x^2\right )}{3\ 2^{2/3} \left (1-16 c_1 x\right ) \sqrt [3]{18432 c_1^2 x^2+\sqrt {4 \left (192 c_1^2 x-12 c_1-256 x^2\right ){}^3+\left (18432 c_1^2 x^2-2880 c_1 x+8192 x^3+108\right ){}^2}-2880 c_1 x+8192 x^3+108}}+\frac {16 x}{3 \left (1-16 c_1 x\right )}\right \},\left \{y(x)\to -\frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{18432 c_1^2 x^2+\sqrt {4 \left (192 c_1^2 x-12 c_1-256 x^2\right ){}^3+\left (18432 c_1^2 x^2-2880 c_1 x+8192 x^3+108\right ){}^2}-2880 c_1 x+8192 x^3+108}}{6 \sqrt [3]{2} \left (1-16 c_1 x\right )}+\frac {\left (1-i \sqrt {3}\right ) \left (192 c_1^2 x-12 c_1-256 x^2\right )}{3\ 2^{2/3} \left (1-16 c_1 x\right ) \sqrt [3]{18432 c_1^2 x^2+\sqrt {4 \left (192 c_1^2 x-12 c_1-256 x^2\right ){}^3+\left (18432 c_1^2 x^2-2880 c_1 x+8192 x^3+108\right ){}^2}-2880 c_1 x+8192 x^3+108}}+\frac {16 x}{3 \left (1-16 c_1 x\right )}\right \}\right \}\]
✓ Maple : cpu = 0.143 (sec), leaf count = 1345
\[ \left \{ y \left ( x \right ) ={\frac {1}{3\,{\it \_C1}+48\,x}\sqrt [3]{4096\,{x}^{3}{{\it \_C1}}^{3}+6\,\sqrt {3}\sqrt {4096\,{{\it \_C1}}^{4}{x}^{3}+27\,{{\it \_C1}}^{4}+576\,x{{\it \_C1}}^{3}+2048\,{{\it \_C1}}^{2}{x}^{2}+16\,{\it \_C1}+256\,x}{\it \_C1}+96\,\sqrt {3}\sqrt {4096\,{{\it \_C1}}^{4}{x}^{3}+27\,{{\it \_C1}}^{4}+576\,x{{\it \_C1}}^{3}+2048\,{{\it \_C1}}^{2}{x}^{2}+16\,{\it \_C1}+256\,x}x+54\,{{\it \_C1}}^{3}+1440\,{{\it \_C1}}^{2}x+9216\,{\it \_C1}\,{x}^{2}}}+{\frac {256\,{{\it \_C1}}^{2}{x}^{2}-12\,{\it \_C1}-192\,x}{3\,{\it \_C1}+48\,x}{\frac {1}{\sqrt [3]{4096\,{x}^{3}{{\it \_C1}}^{3}+6\,\sqrt {3}\sqrt {4096\,{{\it \_C1}}^{4}{x}^{3}+27\,{{\it \_C1}}^{4}+576\,x{{\it \_C1}}^{3}+2048\,{{\it \_C1}}^{2}{x}^{2}+16\,{\it \_C1}+256\,x}{\it \_C1}+96\,\sqrt {3}\sqrt {4096\,{{\it \_C1}}^{4}{x}^{3}+27\,{{\it \_C1}}^{4}+576\,x{{\it \_C1}}^{3}+2048\,{{\it \_C1}}^{2}{x}^{2}+16\,{\it \_C1}+256\,x}x+54\,{{\it \_C1}}^{3}+1440\,{{\it \_C1}}^{2}x+9216\,{\it \_C1}\,{x}^{2}}}}}+{\frac {16\,x{\it \_C1}}{3\,{\it \_C1}+48\,x}},y \left ( x \right ) =-{\frac {1}{6\,{\it \_C1}+96\,x}\sqrt [3]{4096\,{x}^{3}{{\it \_C1}}^{3}+6\,\sqrt {3}\sqrt {4096\,{{\it \_C1}}^{4}{x}^{3}+27\,{{\it \_C1}}^{4}+576\,x{{\it \_C1}}^{3}+2048\,{{\it \_C1}}^{2}{x}^{2}+16\,{\it \_C1}+256\,x}{\it \_C1}+96\,\sqrt {3}\sqrt {4096\,{{\it \_C1}}^{4}{x}^{3}+27\,{{\it \_C1}}^{4}+576\,x{{\it \_C1}}^{3}+2048\,{{\it \_C1}}^{2}{x}^{2}+16\,{\it \_C1}+256\,x}x+54\,{{\it \_C1}}^{3}+1440\,{{\it \_C1}}^{2}x+9216\,{\it \_C1}\,{x}^{2}}}-{\frac {128\,{{\it \_C1}}^{2}{x}^{2}-6\,{\it \_C1}-96\,x}{3\,{\it \_C1}+48\,x}{\frac {1}{\sqrt [3]{4096\,{x}^{3}{{\it \_C1}}^{3}+6\,\sqrt {3}\sqrt {4096\,{{\it \_C1}}^{4}{x}^{3}+27\,{{\it \_C1}}^{4}+576\,x{{\it \_C1}}^{3}+2048\,{{\it \_C1}}^{2}{x}^{2}+16\,{\it \_C1}+256\,x}{\it \_C1}+96\,\sqrt {3}\sqrt {4096\,{{\it \_C1}}^{4}{x}^{3}+27\,{{\it \_C1}}^{4}+576\,x{{\it \_C1}}^{3}+2048\,{{\it \_C1}}^{2}{x}^{2}+16\,{\it \_C1}+256\,x}x+54\,{{\it \_C1}}^{3}+1440\,{{\it \_C1}}^{2}x+9216\,{\it \_C1}\,{x}^{2}}}}}+{\frac {16\,x{\it \_C1}}{3\,{\it \_C1}+48\,x}}-{\frac {i}{2}}\sqrt {3} \left ( {\frac {1}{3\,{\it \_C1}+48\,x}\sqrt [3]{4096\,{x}^{3}{{\it \_C1}}^{3}+6\,\sqrt {3}\sqrt {4096\,{{\it \_C1}}^{4}{x}^{3}+27\,{{\it \_C1}}^{4}+576\,x{{\it \_C1}}^{3}+2048\,{{\it \_C1}}^{2}{x}^{2}+16\,{\it \_C1}+256\,x}{\it \_C1}+96\,\sqrt {3}\sqrt {4096\,{{\it \_C1}}^{4}{x}^{3}+27\,{{\it \_C1}}^{4}+576\,x{{\it \_C1}}^{3}+2048\,{{\it \_C1}}^{2}{x}^{2}+16\,{\it \_C1}+256\,x}x+54\,{{\it \_C1}}^{3}+1440\,{{\it \_C1}}^{2}x+9216\,{\it \_C1}\,{x}^{2}}}-{\frac {256\,{{\it \_C1}}^{2}{x}^{2}-12\,{\it \_C1}-192\,x}{3\,{\it \_C1}+48\,x}{\frac {1}{\sqrt [3]{4096\,{x}^{3}{{\it \_C1}}^{3}+6\,\sqrt {3}\sqrt {4096\,{{\it \_C1}}^{4}{x}^{3}+27\,{{\it \_C1}}^{4}+576\,x{{\it \_C1}}^{3}+2048\,{{\it \_C1}}^{2}{x}^{2}+16\,{\it \_C1}+256\,x}{\it \_C1}+96\,\sqrt {3}\sqrt {4096\,{{\it \_C1}}^{4}{x}^{3}+27\,{{\it \_C1}}^{4}+576\,x{{\it \_C1}}^{3}+2048\,{{\it \_C1}}^{2}{x}^{2}+16\,{\it \_C1}+256\,x}x+54\,{{\it \_C1}}^{3}+1440\,{{\it \_C1}}^{2}x+9216\,{\it \_C1}\,{x}^{2}}}}} \right ) ,y \left ( x \right ) =-{\frac {1}{6\,{\it \_C1}+96\,x}\sqrt [3]{4096\,{x}^{3}{{\it \_C1}}^{3}+6\,\sqrt {3}\sqrt {4096\,{{\it \_C1}}^{4}{x}^{3}+27\,{{\it \_C1}}^{4}+576\,x{{\it \_C1}}^{3}+2048\,{{\it \_C1}}^{2}{x}^{2}+16\,{\it \_C1}+256\,x}{\it \_C1}+96\,\sqrt {3}\sqrt {4096\,{{\it \_C1}}^{4}{x}^{3}+27\,{{\it \_C1}}^{4}+576\,x{{\it \_C1}}^{3}+2048\,{{\it \_C1}}^{2}{x}^{2}+16\,{\it \_C1}+256\,x}x+54\,{{\it \_C1}}^{3}+1440\,{{\it \_C1}}^{2}x+9216\,{\it \_C1}\,{x}^{2}}}-{\frac {128\,{{\it \_C1}}^{2}{x}^{2}-6\,{\it \_C1}-96\,x}{3\,{\it \_C1}+48\,x}{\frac {1}{\sqrt [3]{4096\,{x}^{3}{{\it \_C1}}^{3}+6\,\sqrt {3}\sqrt {4096\,{{\it \_C1}}^{4}{x}^{3}+27\,{{\it \_C1}}^{4}+576\,x{{\it \_C1}}^{3}+2048\,{{\it \_C1}}^{2}{x}^{2}+16\,{\it \_C1}+256\,x}{\it \_C1}+96\,\sqrt {3}\sqrt {4096\,{{\it \_C1}}^{4}{x}^{3}+27\,{{\it \_C1}}^{4}+576\,x{{\it \_C1}}^{3}+2048\,{{\it \_C1}}^{2}{x}^{2}+16\,{\it \_C1}+256\,x}x+54\,{{\it \_C1}}^{3}+1440\,{{\it \_C1}}^{2}x+9216\,{\it \_C1}\,{x}^{2}}}}}+{\frac {16\,x{\it \_C1}}{3\,{\it \_C1}+48\,x}}+{\frac {i}{2}}\sqrt {3} \left ( {\frac {1}{3\,{\it \_C1}+48\,x}\sqrt [3]{4096\,{x}^{3}{{\it \_C1}}^{3}+6\,\sqrt {3}\sqrt {4096\,{{\it \_C1}}^{4}{x}^{3}+27\,{{\it \_C1}}^{4}+576\,x{{\it \_C1}}^{3}+2048\,{{\it \_C1}}^{2}{x}^{2}+16\,{\it \_C1}+256\,x}{\it \_C1}+96\,\sqrt {3}\sqrt {4096\,{{\it \_C1}}^{4}{x}^{3}+27\,{{\it \_C1}}^{4}+576\,x{{\it \_C1}}^{3}+2048\,{{\it \_C1}}^{2}{x}^{2}+16\,{\it \_C1}+256\,x}x+54\,{{\it \_C1}}^{3}+1440\,{{\it \_C1}}^{2}x+9216\,{\it \_C1}\,{x}^{2}}}-{\frac {256\,{{\it \_C1}}^{2}{x}^{2}-12\,{\it \_C1}-192\,x}{3\,{\it \_C1}+48\,x}{\frac {1}{\sqrt [3]{4096\,{x}^{3}{{\it \_C1}}^{3}+6\,\sqrt {3}\sqrt {4096\,{{\it \_C1}}^{4}{x}^{3}+27\,{{\it \_C1}}^{4}+576\,x{{\it \_C1}}^{3}+2048\,{{\it \_C1}}^{2}{x}^{2}+16\,{\it \_C1}+256\,x}{\it \_C1}+96\,\sqrt {3}\sqrt {4096\,{{\it \_C1}}^{4}{x}^{3}+27\,{{\it \_C1}}^{4}+576\,x{{\it \_C1}}^{3}+2048\,{{\it \_C1}}^{2}{x}^{2}+16\,{\it \_C1}+256\,x}x+54\,{{\it \_C1}}^{3}+1440\,{{\it \_C1}}^{2}x+9216\,{\it \_C1}\,{x}^{2}}}}} \right ) \right \} \]