\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac { \left ( {x}^{4}+3\,x \left ( y \left ( x \right ) \right ) ^{2}+3\, \left ( y \left ( x \right ) \right ) ^{2} \right ) y \left ( x \right ) }{ \left ( 6\, \left ( y \left ( x \right ) \right ) ^{2}+x \right ) x \left ( 1+x \right ) }}=0} \]
Mathematica: cpu = 0.696088 (sec), leaf count = 90 \[ \left \{\left \{y(x)\to -\frac {\sqrt {x} \sqrt {W\left (\frac {6 (x+1)^2 e^{2 c_1+x^2-2 x-3}}{x}\right )}}{\sqrt {6}}\right \},\left \{y(x)\to \frac {\sqrt {x} \sqrt {W\left (\frac {6 (x+1)^2 e^{2 c_1+x^2-2 x-3}}{x}\right )}}{\sqrt {6}}\right \}\right \} \]
Maple: cpu = 0.234 (sec), leaf count = 60 \[ \left \{ \left ( \left ( y \left ( x \right ) \right ) ^{-2}+6\,{x}^{-1} \right ) ^{-1}={\frac {x}{54} \left ( {{\rm e}^{{\it RootOf} \left ( { {\rm e}^{{\it \_Z}}}{x}^{2}-{{\rm e}^{{\it \_Z}}}\ln \left ( {\frac {x \left ( {{\rm e}^{{\it \_Z}}}+9 \right ) }{2\, \left ( 1+x \right ) ^{2}} } \right ) +3\,{\it \_C1}\,{{\rm e}^{{\it \_Z}}}+{\it \_Z}\,{{\rm e}^{{ \it \_Z}}}-2\,x{{\rm e}^{{\it \_Z}}}+9 \right ) }}+9 \right ) } \right \} \]