\[ y'(x)=\frac {\left (x y(x)^2+1\right )^3}{x^4 y(x) \left (x y(x)^2+x+1\right )} \] ✓ Mathematica : cpu = 1.04407 (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 = 2.026 (sec), leaf count = 137
\[\left \{\frac {\left (y \left (x \right )-1\right ) \left (2 y \left (x \right )^{4}+2 y \left (x \right )^{2}+1\right ) \left (10 c_{1} x -x \arctan \left (2 y \left (x \right )^{2}+1\right )+x \arctan \left (2 x y \left (x \right )^{4}+\left (2 x +2\right ) y \left (x \right )^{2}+x +1\right )+2 x \ln \left (x y \left (x \right )^{2}-x +1\right )-x \ln \left (2 x^{2} y \left (x \right )^{4}+x^{2}+\left (2 x^{2}+4 x \right ) y \left (x \right )^{2}+2 x +2\right )+5\right ) \left (y \left (x \right )+1\right )}{10 \left (2 y \left (x \right )^{6}-y \left (x \right )^{2}-1\right ) x} = 0\right \}\]