\[ y'(x)=\frac {\left (x y(x)^2+1\right )^3}{x^4 y(x) \left (x y(x)^2+x+1\right )} \] ✓ Mathematica : cpu = 0.877406 (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 = 1.296 (sec), leaf count = 137
\[\frac {\left (-1+y \relax (x )\right ) \left (1+y \relax (x )\right ) \left (2 y \relax (x )^{4}+2 y \relax (x )^{2}+1\right ) \left (2 \ln \left (x y \relax (x )^{2}-x +1\right ) x -\ln \left (2 x^{2} y \relax (x )^{4}+\left (2 x^{2}+4 x \right ) y \relax (x )^{2}+x^{2}+2 x +2\right ) x +\arctan \left (2 x y \relax (x )^{4}+\left (2+2 x \right ) y \relax (x )^{2}+1+x \right ) x -\arctan \left (2 y \relax (x )^{2}+1\right ) x +5 x c_{1}+5\right )}{5 x \left (2 y \relax (x )^{6}-y \relax (x )^{2}-1\right )} = 0\]