\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac { \left ( 3\,x \left ( y \left ( x \right ) \right ) ^{2}+x+3\, \left ( y \left ( x \right ) \right ) ^{2} \right ) y \left ( x \right ) }{ \left ( 6\, \left ( y \left ( x \right ) \right ) ^{2}+x \right ) x \left ( 1+x \right ) }}=0} \]
Mathematica: cpu = 0.570072 (sec), leaf count = 70 \[ \left \{\left \{y(x)\to -\frac {\sqrt {x} \sqrt {W\left (\frac {6 e^{2 c_1} x}{(x+1)^2}\right )}}{\sqrt {6}}\right \},\left \{y(x)\to \frac {\sqrt {x} \sqrt {W\left (\frac {6 e^{2 c_1} x}{(x+1)^2}\right )}}{\sqrt {6}}\right \}\right \} \]
Maple: cpu = 0.234 (sec), leaf count = 51 \[ \left \{ \left ( \left ( y \left ( x \right ) \right ) ^{-2}+6\,{x}^{-1} \right ) ^{-1}={\frac {x}{54} \left ( {{\rm e}^{{\it RootOf} \left ( -{ {\rm e}^{{\it \_Z}}}\ln \left ( {\frac { \left ( 1+x \right ) ^{2} \left ( {{\rm e}^{{\it \_Z}}}+9 \right ) }{2\,x}} \right ) +3\,{\it \_C1 }\,{{\rm e}^{{\it \_Z}}}+{\it \_Z}\,{{\rm e}^{{\it \_Z}}}+9 \right ) }} +9 \right ) } \right \} \]