\[ y'(x)=\frac {2 y(x)^6}{32 x^2 y(x)^4+y(x)^3+16 x y(x)^2+2} \] ✓ Mathematica : cpu = 0.133224 (sec), leaf count = 687
\[\left \{\left \{y(x)\to \frac {2 \sqrt [3]{2} \sqrt [3]{4608 c_1^2 x^2+3 \sqrt {3} \sqrt {\left (1-16 c_1 x\right ){}^2 \left (2048 c_1^2 x^2+64 c_1 \left (4 c_1^3-9\right ) x-16 c_1^3+4096 x^3+27\right )}-720 c_1 x+2048 x^3+27}+\frac {4\ 2^{2/3} \left (-48 c_1^2 x+3 c_1+64 x^2\right )}{\sqrt [3]{4608 c_1^2 x^2+3 \sqrt {3} \sqrt {\left (1-16 c_1 x\right ){}^2 \left (2048 c_1^2 x^2+64 c_1 \left (4 c_1^3-9\right ) x-16 c_1^3+4096 x^3+27\right )}-720 c_1 x+2048 x^3+27}}+32 x}{6 \left (1-16 c_1 x\right )}\right \},\left \{y(x)\to \frac {2 i \sqrt [3]{2} \left (\sqrt {3}+i\right ) \sqrt [3]{4608 c_1^2 x^2+3 \sqrt {3} \sqrt {\left (1-16 c_1 x\right ){}^2 \left (2048 c_1^2 x^2+64 c_1 \left (4 c_1^3-9\right ) x-16 c_1^3+4096 x^3+27\right )}-720 c_1 x+2048 x^3+27}-\frac {4 i 2^{2/3} \left (\sqrt {3}-i\right ) \left (-48 c_1^2 x+3 c_1+64 x^2\right )}{\sqrt [3]{4608 c_1^2 x^2+3 \sqrt {3} \sqrt {\left (1-16 c_1 x\right ){}^2 \left (2048 c_1^2 x^2+64 c_1 \left (4 c_1^3-9\right ) x-16 c_1^3+4096 x^3+27\right )}-720 c_1 x+2048 x^3+27}}+64 x}{12 \left (1-16 c_1 x\right )}\right \},\left \{y(x)\to \frac {-2 \sqrt [3]{2} \left (1+i \sqrt {3}\right ) \sqrt [3]{4608 c_1^2 x^2+3 \sqrt {3} \sqrt {\left (1-16 c_1 x\right ){}^2 \left (2048 c_1^2 x^2+64 c_1 \left (4 c_1^3-9\right ) x-16 c_1^3+4096 x^3+27\right )}-720 c_1 x+2048 x^3+27}+\frac {4 i 2^{2/3} \left (\sqrt {3}+i\right ) \left (-48 c_1^2 x+3 c_1+64 x^2\right )}{\sqrt [3]{4608 c_1^2 x^2+3 \sqrt {3} \sqrt {\left (1-16 c_1 x\right ){}^2 \left (2048 c_1^2 x^2+64 c_1 \left (4 c_1^3-9\right ) x-16 c_1^3+4096 x^3+27\right )}-720 c_1 x+2048 x^3+27}}+64 x}{12 \left (1-16 c_1 x\right )}\right \}\right \}\]
✓ Maple : cpu = 0.132 (sec), leaf count = 1105
\[ \left \{ y \left ( x \right ) ={\frac {1}{96\,x+6\,{\it \_C1}} \left ( 32\,x{\it \_C1}\,\sqrt [3]{96\, \left ( {\it \_C1}/16+x \right ) \sqrt {3}\sqrt { \left ( 4096\,{x}^{3}+27 \right ) {{\it \_C1}}^{4}+576\,x{{\it \_C1}}^{3}+2048\,{{\it \_C1}}^{2}{x}^{2}+16\,{\it \_C1}+256\,x}+ \left ( 4096\,{x}^{3}+54 \right ) {{\it \_C1}}^{3}+1440\,{{\it \_C1}}^{2}x+9216\,{x}^{2}{\it \_C1}}+ \left ( -256\,i{x}^{2}{{\it \_C1}}^{2}+i \left ( 4096\,{x}^{3}{{\it \_C1}}^{3}+6\,\sqrt {3}\sqrt { \left ( 4096\,{x}^{3}+27 \right ) {{\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 { \left ( 4096\,{x}^{3}+27 \right ) {{\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 ) ^{{\frac {2}{3}}}+192\,ix+12\,i{\it \_C1} \right ) \sqrt {3}-256\,{{\it \_C1}}^{2}{x}^{2}- \left ( 4096\,{x}^{3}{{\it \_C1}}^{3}+6\,\sqrt {3}\sqrt { \left ( 4096\,{x}^{3}+27 \right ) {{\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 { \left ( 4096\,{x}^{3}+27 \right ) {{\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 ) ^{{\frac {2}{3}}}+192\,x+12\,{\it \_C1} \right ) {\frac {1}{\sqrt [3]{96\, \left ( {\it \_C1}/16+x \right ) \sqrt {3}\sqrt { \left ( 4096\,{x}^{3}+27 \right ) {{\it \_C1}}^{4}+576\,x{{\it \_C1}}^{3}+2048\,{{\it \_C1}}^{2}{x}^{2}+16\,{\it \_C1}+256\,x}+ \left ( 4096\,{x}^{3}+54 \right ) {{\it \_C1}}^{3}+1440\,{{\it \_C1}}^{2}x+9216\,{x}^{2}{\it \_C1}}}}},y \left ( x \right ) =-{\frac {1}{96\,x+6\,{\it \_C1}} \left ( -32\,x{\it \_C1}\,\sqrt [3]{96\, \left ( {\it \_C1}/16+x \right ) \sqrt {3}\sqrt { \left ( 4096\,{x}^{3}+27 \right ) {{\it \_C1}}^{4}+576\,x{{\it \_C1}}^{3}+2048\,{{\it \_C1}}^{2}{x}^{2}+16\,{\it \_C1}+256\,x}+ \left ( 4096\,{x}^{3}+54 \right ) {{\it \_C1}}^{3}+1440\,{{\it \_C1}}^{2}x+9216\,{x}^{2}{\it \_C1}}+ \left ( -256\,i{x}^{2}{{\it \_C1}}^{2}+i \left ( 4096\,{x}^{3}{{\it \_C1}}^{3}+6\,\sqrt {3}\sqrt { \left ( 4096\,{x}^{3}+27 \right ) {{\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 { \left ( 4096\,{x}^{3}+27 \right ) {{\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 ) ^{{\frac {2}{3}}}+192\,ix+12\,i{\it \_C1} \right ) \sqrt {3}+256\,{{\it \_C1}}^{2}{x}^{2}+ \left ( 4096\,{x}^{3}{{\it \_C1}}^{3}+6\,\sqrt {3}\sqrt { \left ( 4096\,{x}^{3}+27 \right ) {{\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 { \left ( 4096\,{x}^{3}+27 \right ) {{\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 ) ^{{\frac {2}{3}}}-192\,x-12\,{\it \_C1} \right ) {\frac {1}{\sqrt [3]{96\, \left ( {\it \_C1}/16+x \right ) \sqrt {3}\sqrt { \left ( 4096\,{x}^{3}+27 \right ) {{\it \_C1}}^{4}+576\,x{{\it \_C1}}^{3}+2048\,{{\it \_C1}}^{2}{x}^{2}+16\,{\it \_C1}+256\,x}+ \left ( 4096\,{x}^{3}+54 \right ) {{\it \_C1}}^{3}+1440\,{{\it \_C1}}^{2}x+9216\,{x}^{2}{\it \_C1}}}}},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\,{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\,{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\,{x}^{2}{\it \_C1}}}}}+16\,{\frac {x{\it \_C1}}{3\,{\it \_C1}+48\,x}} \right \} \]