\[ y'(x)=\frac {(y(x)+1) (2 y(x)+1)}{x \left (2 x y(x)^4+x y(x)^3-2 y(x)-2\right )} \] ✓ Mathematica : cpu = 0.393136 (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 = 0.896 (sec), leaf count = 54
\[ \left \{ y \left ( x \right ) ={\frac {1}{2}{{\rm e}^{{\it RootOf} \left ( x \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{3}-8\,x \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{2}+16\,\ln \left ( 1/2\,{{\rm e}^{{\it \_Z}}}+1/2 \right ) x{{\rm e}^{{\it \_Z}}}+8\,{\it \_C1}\,x{{\rm e}^{{\it \_Z}}}-2\,{\it \_Z}\,x{{\rm e}^{{\it \_Z}}}+7\,x{{\rm e}^{{\it \_Z}}}+16 \right ) }}}-{\frac {1}{2}} \right \} \]