\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =1/2\,{\frac {{x}^{3}+{x}^{2}+2\,\sqrt {{x}^{3}-6\,y \left ( x \right ) }}{1+x}}=0} \]
Mathematica: cpu = 0.180523 (sec), leaf count = 35 \[ \left \{\left \{y(x)\to \frac {1}{6} \left (18 c_1 \log (x+1)-9 c_1^2+x^3-9 \log ^2(x+1)\right )\right \}\right \} \]
Maple: cpu = 0.202 (sec), leaf count = 23 \[ \left \{ {\it \_C1}-3\,\ln \left ( 1+x \right ) -\sqrt {{x}^{3}-6\,y \left ( x \right ) }=0 \right \} \]