\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac { \left ( 1+2\,y \left ( x \right ) \right ) \left ( 1+y \left ( x \right ) \right ) }{x \left ( -2\,y \left ( x \right ) -2+x \left ( y \left ( x \right ) \right ) ^{3}+2\,x \left ( y \left ( x \right ) \right ) ^{4} \right ) }}=0} \]
Mathematica: cpu = 0.208027 (sec), leaf count = 56 \[ \text {Solve}\left [-\frac {1}{8} y(x)^2+\frac {3 y(x)}{8}-\frac {1}{2 x (2 y(x)+1)}-\frac {1}{2} \log (y(x)+1)+\frac {1}{16} \log (2 y(x)+1)=c_1,y(x)\right ] \]
Maple: cpu = 0.202 (sec), leaf count = 54 \[ \left \{ y \left ( x \right ) ={\frac {1}{2}{{\rm e}^{{\it RootOf} \left ( x \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{3}-8\,x \left ( { {\rm e}^{{\it \_Z}}} \right ) ^{2}+16\,\ln \left ( 1/2\,{{\rm e}^{{\it \_Z}}}+1/2 \right ) x{{\rm e}^{{\it \_Z}}}+16\,{\it \_C1}\,{{\rm e}^{{ \it \_Z}}}x-2\,{{\rm e}^{{\it \_Z}}}{\it \_Z}\,x+7\,x{{\rm e}^{{\it \_Z}}}+16 \right ) }}}-{\frac {1}{2}} \right \} \]