\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =2\,{\frac { \left ( y \left ( x \right ) \right ) ^{6}}{ \left ( y \left ( x \right ) \right ) ^{3}+2+16\,x \left ( y \left ( x \right ) \right ) ^{2}+32\,{x}^{2} \left ( y \left ( x \right ) \right ) ^{4}}}=0} \]
Mathematica: cpu = 0.105513 (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 = 0.094 (sec), leaf count = 1345 \[ \left \{ y \left ( x \right ) ={\frac {1}{3\,{\it \_C1}+48\,x}\sqrt [3]{ 4096\,{{\it \_C1}}^{3}{x}^{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\,{x}^{2}{\it \_C1}}}+{\frac {256\,{{ \it \_C1}}^{2}{x}^{2}-12\,{\it \_C1}-192\,x}{3\,{\it \_C1}+48\,x}{ \frac {1}{\sqrt [3]{4096\,{{\it \_C1}}^{3}{x}^{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\,{x}^{2}{ \it \_C1}}}}}+{\frac {16\,{\it \_C1}\,x}{3\,{\it \_C1}+48\,x}},y \left ( x \right ) =-{\frac {1}{6\,{\it \_C1}+96\,x}\sqrt [3]{4096\,{{ \it \_C1}}^{3}{x}^{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\,{x}^{2}{\it \_C1}}}-{\frac {128\,{{\it \_C1}}^{2}{x}^{2}-6\,{\it \_C1}-96\,x}{3\,{\it \_C1}+48\,x}{\frac {1}{ \sqrt [3]{4096\,{{\it \_C1}}^{3}{x}^{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\,{x}^{2}{\it \_C1}}} }}+{\frac {16\,{\it \_C1}\,x}{3\,{\it \_C1}+48\,x}}-{\frac {i}{2}} \sqrt {3} \left ( {\frac {1}{3\,{\it \_C1}+48\,x}\sqrt [3]{4096\,{{\it \_C1}}^{3}{x}^{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\,{x}^{2}{\it \_C1}}}-{\frac {256\,{{\it \_C1}}^{2}{x}^{2}-12\,{\it \_C1}-192\,x}{3\,{\it \_C1}+48\,x}{\frac {1 }{\sqrt [3]{4096\,{{\it \_C1}}^{3}{x}^{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\,{x}^{2}{\it \_C1}}} }} \right ) ,y \left ( x \right ) =-{\frac {1}{6\,{\it \_C1}+96\,x}\sqrt [3]{4096\,{{\it \_C1}}^{3}{x}^{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\,{x}^{2}{\it \_C1}}}-{\frac { 128\,{{\it \_C1}}^{2}{x}^{2}-6\,{\it \_C1}-96\,x}{3\,{\it \_C1}+48\,x} {\frac {1}{\sqrt [3]{4096\,{{\it \_C1}}^{3}{x}^{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\,{x}^{2}{ \it \_C1}}}}}+{\frac {16\,{\it \_C1}\,x}{3\,{\it \_C1}+48\,x}}+{\frac {i}{2}}\sqrt {3} \left ( {\frac {1}{3\,{\it \_C1}+48\,x}\sqrt [3]{4096 \,{{\it \_C1}}^{3}{x}^{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\,{x}^{2}{\it \_C1}}}-{\frac {256\,{{\it \_C1}}^{2}{x}^{2}-12\,{\it \_C1}-192\,x}{3\,{\it \_C1}+48\,x}{\frac {1 }{\sqrt [3]{4096\,{{\it \_C1}}^{3}{x}^{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\,{x}^{2}{\it \_C1}}} }} \right ) \right \} \]