\[ y'(x)=\frac {x \left (-x^6+3 x^4 y(x)^2+x^4-3 x^2 y(x)^4-2 x^2 y(x)^2+y(x)^6+y(x)^4+1\right )}{y(x)} \] ✓ Mathematica : cpu = 0.725771 (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 = 0.42 (sec), leaf count = 107
\[y \relax (x ) = {\mathrm e}^{\RootOf \left (-3 x^{2} {\mathrm e}^{2 \textit {\_Z}}+6 x^{3} {\mathrm e}^{\textit {\_Z}}+3 \,{\mathrm e}^{2 \textit {\_Z}} \ln \left (\frac {{\mathrm e}^{2 \textit {\_Z}}-2 \,{\mathrm e}^{\textit {\_Z}} x +1}{{\mathrm e}^{\textit {\_Z}}-2 x}\right )-2 c_{1} {\mathrm e}^{2 \textit {\_Z}}-3 \textit {\_Z} \,{\mathrm e}^{2 \textit {\_Z}}-6 \,{\mathrm e}^{\textit {\_Z}} \ln \left (\frac {{\mathrm e}^{2 \textit {\_Z}}-2 \,{\mathrm e}^{\textit {\_Z}} x +1}{{\mathrm e}^{\textit {\_Z}}-2 x}\right ) x +4 c_{1} x \,{\mathrm e}^{\textit {\_Z}}+6 \textit {\_Z} x \,{\mathrm e}^{\textit {\_Z}}-3\right )}-x\]