\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =-{\frac { \left ( -1- \left ( y \left ( x \right ) \right ) ^{4}+2\,{x}^{2} \left ( y \left ( x \right ) \right ) ^{2}-{x}^{4}- \left ( y \left ( x \right ) \right ) ^{6}+3\,{x}^{2} \left ( y \left ( x \right ) \right ) ^{4}-3\,{x}^{4} \left ( y \left ( x \right ) \right ) ^{2}+{x}^{6} \right ) x}{y \left ( x \right ) }}=0} \]
Mathematica: cpu = 0.364546 (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 = 0.265 (sec), leaf count = 107 \[ \left \{ y \left ( x \right ) ={{\rm e}^{{\it RootOf} \left ( -3\,{x}^{2} \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{2}+6\,{x}^{3}{{\rm e}^{{\it \_Z}}}+3\, \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{2}\ln \left ( { \frac { \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{2}-2\,x{{\rm e}^{{\it \_Z}}}+1}{{{\rm e}^{{\it \_Z}}}-2\,x}} \right ) -2\,{\it \_C1}\, \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{2}-3\,{\it \_Z}\, \left ( { {\rm e}^{{\it \_Z}}} \right ) ^{2}-6\,{{\rm e}^{{\it \_Z}}}\ln \left ( {\frac { \left ( {{\rm e}^{{\it \_Z}}} \right ) ^{2}-2\,x{{\rm e}^{{\it \_Z}}}+1}{{{\rm e}^{{\it \_Z}}}-2\,x}} \right ) x+4\,{\it \_C1}\,{ {\rm e}^{{\it \_Z}}}x+6\,{{\rm e}^{{\it \_Z}}}{\it \_Z}\,x-3 \right ) } }-x \right \} \]