\[ \boxed { \left ( 6\,xy \left ( x \right ) +{x}^{2}+3 \right ) {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) +3\, \left ( y \left ( x \right ) \right ) ^{2}+2\,xy \left ( x \right ) +2\,x=0} \]
Mathematica: cpu = 0.013002 (sec), leaf count = 106 \[ \left \{\left \{y(x)\to -\frac {\sqrt {6 c_1 x-2 x^3+\frac {1}{6} \left (x^2+3\right )^2}}{\sqrt {6} x}-\frac {x^2+3}{6 x}\right \},\left \{y(x)\to \frac {\sqrt {6 c_1 x-2 x^3+\frac {1}{6} \left (x^2+3\right )^2}}{\sqrt {6} x}-\frac {x^2+3}{6 x}\right \}\right \} \]
Maple: cpu = 0.016 (sec), leaf count = 71 \[ \left \{ y \left ( x \right ) ={\frac {1}{6\,x} \left ( -{x}^{2}-3+\sqrt {{x}^{4}-12\,{x}^{3}-12\,{\it \_C1}\,x+6\,{x}^{2}+9} \right ) },y \left ( x \right ) =-{\frac {1}{6\,x} \left ( {x}^{2}+\sqrt {{x}^{4}-12 \,{x}^{3}-12\,{\it \_C1}\,x+6\,{x}^{2}+9}+3 \right ) } \right \} \]