\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) = \left ( y \left ( x \right ) +2+\sqrt {3\,x+1} \right ) ^{-1}=0} \]
Mathematica: cpu = 0.449057 (sec), leaf count = 134 \[ \text {Solve}\left [44 c_1+6 \sqrt {33} \tanh ^{-1}\left (\frac {3 y(x)+7 \sqrt {3 x+1}+6}{\sqrt {33} \left (y(x)+\sqrt {3 x+1}+2\right )}\right )=33 \left (\log \left (\left (y(x)+\sqrt {3 x+1}+2\right )^2 \left (\frac {1}{\left (y(x)+\sqrt {3 x+1}+2\right )^2}+\frac {3}{2 \sqrt {3 x+1} \left (y(x)+\sqrt {3 x+1}+2\right )}-\frac {3}{6 x+2}\right )\right )+\log (12 x+4)\right ),y(x)\right ] \]
Maple: cpu = 0.172 (sec), leaf count = 83 \[ \left \{ \ln \left ( 3\,\sqrt {3\,x+1}y \left ( x \right ) +3\, \left ( y \left ( x \right ) \right ) ^{2}+6\,\sqrt {3\,x+1}-6\,x+12\,y \left ( x \right ) +10 \right ) -6\,{\frac {\sqrt {3\,x+1}}{\sqrt {99\,x+33}}{ \it Artanh} \left ( {\frac {3\,\sqrt {3\,x+1}+6\,y \left ( x \right ) +12 }{\sqrt {99\,x+33}}} \right ) }-{\it \_C1}=0 \right \} \]