\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac { \left ( x \left ( y \left ( x \right ) \right ) ^{2}+1 \right ) ^{3}}{{x}^{4} \left ( x \left ( y \left ( x \right ) \right ) ^{2}+1+x \right ) y \left ( x \right ) }}=0} \]
Mathematica: cpu = 1.559198 (sec), leaf count = 112 \[ \text {Solve}\left [2 \left (\frac {1}{10} \log \left (2 x^2 y(x)^4+2 x^2 y(x)^2+x^2+4 x y(x)^2+2 x+2\right )-\frac {1}{5} \log \left (x y(x)^2-x+1\right )-\frac {1}{10} \tan ^{-1}\left (2 x y(x)^4+2 x y(x)^2+2 y(x)^2+x+1\right )-\frac {1}{2 x}\right )+\frac {1}{5} \tan ^{-1}\left (2 y(x)^2+1\right )=c_1,y(x)\right ] \]
Maple: cpu = 1.685 (sec), leaf count = 475 \[ \left \{ {\frac {\ln \left ( x \left ( y \left ( x \right ) \right ) ^{2} -x+1 \right ) \left ( y \left ( x \right ) \right ) ^{2}}{5\, \left ( y \left ( x \right ) \right ) ^{2}-5}}-{\frac {\ln \left ( x \left ( y \left ( x \right ) \right ) ^{2}-x+1 \right ) }{5\, \left ( y \left ( x \right ) \right ) ^{2}-5}}+{\frac {1}{2\,x}}-{\frac {\ln \left ( 2\,{x }^{2} \left ( y \left ( x \right ) \right ) ^{4}+2\,{x}^{2} \left ( y \left ( x \right ) \right ) ^{2}+4\,x \left ( y \left ( x \right ) \right ) ^{2}+{x}^{2}+2\,x+2 \right ) \left ( y \left ( x \right ) \right ) ^{4}}{10\, \left ( y \left ( x \right ) \right ) ^{4}+10\, \left ( y \left ( x \right ) \right ) ^{2}+5}}-{\frac {\ln \left ( 2\,{x }^{2} \left ( y \left ( x \right ) \right ) ^{4}+2\,{x}^{2} \left ( y \left ( x \right ) \right ) ^{2}+4\,x \left ( y \left ( x \right ) \right ) ^{2}+{x}^{2}+2\,x+2 \right ) \left ( y \left ( x \right ) \right ) ^{2}}{10\, \left ( y \left ( x \right ) \right ) ^{4}+10\, \left ( y \left ( x \right ) \right ) ^{2}+5}}-{\frac {\ln \left ( 2\,{x }^{2} \left ( y \left ( x \right ) \right ) ^{4}+2\,{x}^{2} \left ( y \left ( x \right ) \right ) ^{2}+4\,x \left ( y \left ( x \right ) \right ) ^{2}+{x}^{2}+2\,x+2 \right ) }{20\, \left ( y \left ( x \right ) \right ) ^{4}+20\, \left ( y \left ( x \right ) \right ) ^{2}+10}}-{ \frac {2\,\arctan \left ( \left ( 2\, \left ( y \left ( x \right ) \right ) ^{4}+2\, \left ( y \left ( x \right ) \right ) ^{2}+1 \right ) x+ 2\, \left ( y \left ( x \right ) \right ) ^{2}+1 \right ) \left ( y \left ( x \right ) \right ) ^{2}}{5}}-{\frac {\arctan \left ( \left ( 2 \, \left ( y \left ( x \right ) \right ) ^{4}+2\, \left ( y \left ( x \right ) \right ) ^{2}+1 \right ) x+2\, \left ( y \left ( x \right ) \right ) ^{2}+1 \right ) }{10}}+{\frac {4\,\arctan \left ( \left ( 2\, \left ( y \left ( x \right ) \right ) ^{4}+2\, \left ( y \left ( x \right ) \right ) ^{2}+1 \right ) x+2\, \left ( y \left ( x \right ) \right ) ^{2}+1 \right ) \left ( y \left ( x \right ) \right ) ^{6}}{10\, \left ( y \left ( x \right ) \right ) ^{4}+10\, \left ( y \left ( x \right ) \right ) ^{2}+5}}+{\frac {6\,\arctan \left ( \left ( 2\, \left ( y \left ( x \right ) \right ) ^{4}+2\, \left ( y \left ( x \right ) \right ) ^{2}+1 \right ) x+2\, \left ( y \left ( x \right ) \right ) ^{2}+1 \right ) \left ( y \left ( x \right ) \right ) ^{4}}{10\, \left ( y \left ( x \right ) \right ) ^{4}+10\, \left ( y \left ( x \right ) \right ) ^{2}+5}}+{\frac {4\,\arctan \left ( \left ( 2\, \left ( y \left ( x \right ) \right ) ^{4}+2\, \left ( y \left ( x \right ) \right ) ^{2}+1 \right ) x+2\, \left ( y \left ( x \right ) \right ) ^{2}+1 \right ) \left ( y \left ( x \right ) \right ) ^{2}}{10\, \left ( y \left ( x \right ) \right ) ^{4}+10\, \left ( y \left ( x \right ) \right ) ^{2}+5}}+{\frac {\arctan \left ( \left ( 2\, \left ( y \left ( x \right ) \right ) ^{4}+2\, \left ( y \left ( x \right ) \right ) ^{2}+1 \right ) x+2\, \left ( y \left ( x \right ) \right ) ^{2}+ 1 \right ) }{10\, \left ( y \left ( x \right ) \right ) ^{4}+10\, \left ( y \left ( x \right ) \right ) ^{2}+5}}-{\frac {\arctan \left ( 2\, \left ( y \left ( x \right ) \right ) ^{2}+1 \right ) }{10}}+{\it \_C1}=0 \right \} \]