\[ y'(x)=\frac {2 y(x)^6}{32 x^2 y(x)^4+y(x)^3+16 x y(x)^2+2} \] ✓ Mathematica : cpu = 0.247344 (sec), leaf count = 705
\[\left \{\left \{y(x)\to \frac {\sqrt [3]{8192 x^3+18432 c_1{}^2 x^2+\sqrt {4 \left (-256 x^2+192 c_1{}^2 x-12 c_1\right ){}^3+\left (8192 x^3+18432 c_1{}^2 x^2-2880 c_1 x+108\right ){}^2}-2880 c_1 x+108}}{3 \sqrt [3]{2} (1-16 c_1 x)}-\frac {\sqrt [3]{2} \left (-256 x^2+192 c_1{}^2 x-12 c_1\right )}{3 (1-16 c_1 x) \sqrt [3]{8192 x^3+18432 c_1{}^2 x^2+\sqrt {4 \left (-256 x^2+192 c_1{}^2 x-12 c_1\right ){}^3+\left (8192 x^3+18432 c_1{}^2 x^2-2880 c_1 x+108\right ){}^2}-2880 c_1 x+108}}+\frac {16 x}{3 (1-16 c_1 x)}\right \},\left \{y(x)\to -\frac {\left (1-i \sqrt {3}\right ) \sqrt [3]{8192 x^3+18432 c_1{}^2 x^2+\sqrt {4 \left (-256 x^2+192 c_1{}^2 x-12 c_1\right ){}^3+\left (8192 x^3+18432 c_1{}^2 x^2-2880 c_1 x+108\right ){}^2}-2880 c_1 x+108}}{6 \sqrt [3]{2} (1-16 c_1 x)}+\frac {\left (1+i \sqrt {3}\right ) \left (-256 x^2+192 c_1{}^2 x-12 c_1\right )}{3\ 2^{2/3} (1-16 c_1 x) \sqrt [3]{8192 x^3+18432 c_1{}^2 x^2+\sqrt {4 \left (-256 x^2+192 c_1{}^2 x-12 c_1\right ){}^3+\left (8192 x^3+18432 c_1{}^2 x^2-2880 c_1 x+108\right ){}^2}-2880 c_1 x+108}}+\frac {16 x}{3 (1-16 c_1 x)}\right \},\left \{y(x)\to -\frac {\left (1+i \sqrt {3}\right ) \sqrt [3]{8192 x^3+18432 c_1{}^2 x^2+\sqrt {4 \left (-256 x^2+192 c_1{}^2 x-12 c_1\right ){}^3+\left (8192 x^3+18432 c_1{}^2 x^2-2880 c_1 x+108\right ){}^2}-2880 c_1 x+108}}{6 \sqrt [3]{2} (1-16 c_1 x)}+\frac {\left (1-i \sqrt {3}\right ) \left (-256 x^2+192 c_1{}^2 x-12 c_1\right )}{3\ 2^{2/3} (1-16 c_1 x) \sqrt [3]{8192 x^3+18432 c_1{}^2 x^2+\sqrt {4 \left (-256 x^2+192 c_1{}^2 x-12 c_1\right ){}^3+\left (8192 x^3+18432 c_1{}^2 x^2-2880 c_1 x+108\right ){}^2}-2880 c_1 x+108}}+\frac {16 x}{3 (1-16 c_1 x)}\right \}\right \}\] ✓ Maple : cpu = 0.141 (sec), leaf count = 1105
\[\left \{y \left (x \right ) = \frac {-256 c_{1}^{2} x^{2}+32 c_{1} \left (\left (4096 x^{3}+54\right ) c_{1}^{3}+1440 c_{1}^{2} x +9216 c_{1} x^{2}+96 \left (\frac {c_{1}}{16}+x \right ) \sqrt {3}\, \sqrt {\left (4096 x^{3}+27\right ) c_{1}^{4}+576 c_{1}^{3} x +2048 c_{1}^{2} x^{2}+16 c_{1}+256 x}\right )^{\frac {1}{3}} x +12 c_{1}+192 x +\left (-256 i c_{1}^{2} x^{2}+12 i c_{1}+192 i x +i \left (4096 c_{1}^{3} x^{3}+54 c_{1}^{3}+1440 c_{1}^{2} x +9216 c_{1} x^{2}+6 c_{1} \sqrt {3}\, \sqrt {\left (4096 x^{3}+27\right ) c_{1}^{4}+576 c_{1}^{3} x +2048 c_{1}^{2} x^{2}+16 c_{1}+256 x}+96 \sqrt {3}\, \sqrt {\left (4096 x^{3}+27\right ) c_{1}^{4}+576 c_{1}^{3} x +2048 c_{1}^{2} x^{2}+16 c_{1}+256 x}\, x \right )^{\frac {2}{3}}\right ) \sqrt {3}-\left (4096 c_{1}^{3} x^{3}+54 c_{1}^{3}+1440 c_{1}^{2} x +9216 c_{1} x^{2}+6 c_{1} \sqrt {3}\, \sqrt {\left (4096 x^{3}+27\right ) c_{1}^{4}+576 c_{1}^{3} x +2048 c_{1}^{2} x^{2}+16 c_{1}+256 x}+96 \sqrt {3}\, \sqrt {\left (4096 x^{3}+27\right ) c_{1}^{4}+576 c_{1}^{3} x +2048 c_{1}^{2} x^{2}+16 c_{1}+256 x}\, x \right )^{\frac {2}{3}}}{\left (\left (4096 x^{3}+54\right ) c_{1}^{3}+1440 c_{1}^{2} x +9216 c_{1} x^{2}+96 \left (\frac {c_{1}}{16}+x \right ) \sqrt {3}\, \sqrt {\left (4096 x^{3}+27\right ) c_{1}^{4}+576 c_{1}^{3} x +2048 c_{1}^{2} x^{2}+16 c_{1}+256 x}\right )^{\frac {1}{3}} \left (6 c_{1}+96 x \right )}, y \left (x \right ) = -\frac {256 c_{1}^{2} x^{2}-32 c_{1} \left (\left (4096 x^{3}+54\right ) c_{1}^{3}+1440 c_{1}^{2} x +9216 c_{1} x^{2}+96 \left (\frac {c_{1}}{16}+x \right ) \sqrt {3}\, \sqrt {\left (4096 x^{3}+27\right ) c_{1}^{4}+576 c_{1}^{3} x +2048 c_{1}^{2} x^{2}+16 c_{1}+256 x}\right )^{\frac {1}{3}} x -12 c_{1}-192 x +\left (-256 i c_{1}^{2} x^{2}+12 i c_{1}+192 i x +i \left (4096 c_{1}^{3} x^{3}+54 c_{1}^{3}+1440 c_{1}^{2} x +9216 c_{1} x^{2}+6 c_{1} \sqrt {3}\, \sqrt {\left (4096 x^{3}+27\right ) c_{1}^{4}+576 c_{1}^{3} x +2048 c_{1}^{2} x^{2}+16 c_{1}+256 x}+96 \sqrt {3}\, \sqrt {\left (4096 x^{3}+27\right ) c_{1}^{4}+576 c_{1}^{3} x +2048 c_{1}^{2} x^{2}+16 c_{1}+256 x}\, x \right )^{\frac {2}{3}}\right ) \sqrt {3}+\left (4096 c_{1}^{3} x^{3}+54 c_{1}^{3}+1440 c_{1}^{2} x +9216 c_{1} x^{2}+6 c_{1} \sqrt {3}\, \sqrt {\left (4096 x^{3}+27\right ) c_{1}^{4}+576 c_{1}^{3} x +2048 c_{1}^{2} x^{2}+16 c_{1}+256 x}+96 \sqrt {3}\, \sqrt {\left (4096 x^{3}+27\right ) c_{1}^{4}+576 c_{1}^{3} x +2048 c_{1}^{2} x^{2}+16 c_{1}+256 x}\, x \right )^{\frac {2}{3}}}{\left (\left (4096 x^{3}+54\right ) c_{1}^{3}+1440 c_{1}^{2} x +9216 c_{1} x^{2}+96 \left (\frac {c_{1}}{16}+x \right ) \sqrt {3}\, \sqrt {\left (4096 x^{3}+27\right ) c_{1}^{4}+576 c_{1}^{3} x +2048 c_{1}^{2} x^{2}+16 c_{1}+256 x}\right )^{\frac {1}{3}} \left (6 c_{1}+96 x \right )}, y \left (x \right ) = \frac {16 c_{1} x}{3 c_{1}+48 x}+\frac {\left (4096 c_{1}^{3} x^{3}+54 c_{1}^{3}+1440 c_{1}^{2} x +9216 c_{1} x^{2}+6 c_{1} \sqrt {3}\, \sqrt {4096 c_{1}^{4} x^{3}+2048 c_{1}^{2} x^{2}+576 c_{1}^{3} x +27 c_{1}^{4}+256 x +16 c_{1}}+96 \sqrt {3}\, \sqrt {4096 c_{1}^{4} x^{3}+2048 c_{1}^{2} x^{2}+576 c_{1}^{3} x +27 c_{1}^{4}+256 x +16 c_{1}}\, x \right )^{\frac {1}{3}}}{3 c_{1}+48 x}+\frac {\frac {256}{3} c_{1}^{2} x^{2}-64 x -4 c_{1}}{\left (c_{1}+16 x \right ) \left (4096 c_{1}^{3} x^{3}+54 c_{1}^{3}+1440 c_{1}^{2} x +9216 c_{1} x^{2}+6 c_{1} \sqrt {3}\, \sqrt {4096 c_{1}^{4} x^{3}+2048 c_{1}^{2} x^{2}+576 c_{1}^{3} x +27 c_{1}^{4}+256 x +16 c_{1}}+96 \sqrt {3}\, \sqrt {4096 c_{1}^{4} x^{3}+2048 c_{1}^{2} x^{2}+576 c_{1}^{3} x +27 c_{1}^{4}+256 x +16 c_{1}}\, x \right )^{\frac {1}{3}}}\right \}\]