\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac { \left ( {x}^{4}+{x}^{3}+x+3\, \left ( y \left ( x \right ) \right ) ^{2} \right ) y \left ( x \right ) }{ \left ( 6\, \left ( y \left ( x \right ) \right ) ^{2}+x \right ) x}}=0} \]
Mathematica: cpu = 0.495563 (sec), leaf count = 82 \[ \left \{\left \{y(x)\to -\frac {\sqrt {x} \sqrt {W\left (6 x e^{2 c_1+\frac {2 x^3}{3}+x^2}\right )}}{\sqrt {6}}\right \},\left \{y(x)\to \frac {\sqrt {x} \sqrt {W\left (6 x e^{2 c_1+\frac {2 x^3}{3}+x^2}\right )}}{\sqrt {6}}\right \}\right \} \]
Maple: cpu = 0.249 (sec), leaf count = 61 \[ \left \{ \left ( \left ( y \left ( x \right ) \right ) ^{-2}+6\,{x}^{-1} \right ) ^{-1}={\frac {x}{54} \left ( {{\rm e}^{{\it RootOf} \left ( 2\, {x}^{3}{{\rm e}^{{\it \_Z}}}+3\,{{\rm e}^{{\it \_Z}}}{x}^{2}-3\,{ {\rm e}^{{\it \_Z}}}\ln \left ( 1/2\,{\frac {{{\rm e}^{{\it \_Z}}}+9}{ x}} \right ) +9\,{{\rm e}^{{\it \_Z}}}{\it \_C1}+3\,{\it \_Z}\,{{\rm e} ^{{\it \_Z}}}+27 \right ) }}+9 \right ) } \right \} \]