\[ y'(x)=\frac {\left (x y(x)^2+1\right )^3}{x^4 y(x) \left (x y(x)^2+x+1\right )} \] ✓ Mathematica : cpu = 2.38317 (sec), leaf count = 85
\[\text {Solve}\left [5 \left (c_1+\frac {1}{x}\right )+2 \log \left (x y(x)^2-x+1\right )+\tan ^{-1}\left (2 x y(x)^4+2 (x+1) y(x)^2+x+1\right )=\log \left (2 x^2 y(x)^4+x^2+2 x (x+2) y(x)^2+2 x+2\right )+\tan ^{-1}\left (2 y(x)^2+1\right ),y(x)\right ]\]
✓ Maple : cpu = 1.388 (sec), leaf count = 137
\[ \left \{ {\frac { \left ( 2\, \left ( y \left ( x \right ) \right ) ^{4}+2\, \left ( y \left ( x \right ) \right ) ^{2}+1 \right ) \left ( -1+y \left ( x \right ) \right ) \left ( 1+y \left ( x \right ) \right ) \left ( 2\,\ln \left ( x \left ( y \left ( x \right ) \right ) ^{2}-x+1 \right ) x-\ln \left ( 2\,{x}^{2} \left ( y \left ( x \right ) \right ) ^{4}+ \left ( 2\,{x}^{2}+4\,x \right ) \left ( y \left ( x \right ) \right ) ^{2}+{x}^{2}+2\,x+2 \right ) x+\arctan \left ( 2\,x \left ( y \left ( x \right ) \right ) ^{4}+ \left ( 2+2\,x \right ) \left ( y \left ( x \right ) \right ) ^{2}+1+x \right ) x-\arctan \left ( 2\, \left ( y \left ( x \right ) \right ) ^{2}+1 \right ) x+5\,x{\it \_C1}+5 \right ) }{5\,x \left ( 2\, \left ( y \left ( x \right ) \right ) ^{6}- \left ( y \left ( x \right ) \right ) ^{2}-1 \right ) }}=0 \right \} \]