\[ y'(x)=-\frac {x \left (-3 x^4 y(x)^2+3 x^2 y(x)^4+2 x^2 y(x)^2+x^6-x^4-y(x)^6-y(x)^4-1\right )}{y(x)} \] ✓ Mathematica : cpu = 0.543185 (sec), leaf count = 71
\[\text {Solve}\left [\frac {1}{4} \left (2 \log \left (-x^2+y(x)^2+1\right )-2 x^2-\frac {1}{y(x) (y(x)+x)}+\frac {1}{x y(x)-y(x)^2}-2 \log (x-y(x))-2 \log (y(x)+x)\right )=c_1,y(x)\right ]\] ✓ Maple : cpu = 1.041 (sec), leaf count = 107
\[ \left \{ y \left ( x \right ) =-{{\rm e}^{{\it RootOf} \left ( 3\,{x}^{2} \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{2}-6\,{x}^{3}{{\rm e}^{{\it \_Z}}}-3\, \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{2}\ln \left ( {\frac { \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{2}-2\,x{{\rm e}^{{\it \_Z}}}+1}{{{\rm e}^{{\it \_Z}}}-2\,x}} \right ) -2\, \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{2}{\it \_C1}+3\,{\it \_Z}\, \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{2}+6\,{{\rm e}^{{\it \_Z}}}\ln \left ( {\frac { \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{2}-2\,x{{\rm e}^{{\it \_Z}}}+1}{{{\rm e}^{{\it \_Z}}}-2\,x}} \right ) x+4\,{\it \_C1}\,x{{\rm e}^{{\it \_Z}}}-6\,{\it \_Z}\,x{{\rm e}^{{\it \_Z}}}+3 \right ) }}+x \right \} \]