\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =1/2\,{\frac {{x}^{2} \left ( x+1+2\,x\sqrt {{x}^{3}-6\,y \left ( x \right ) } \right ) }{1+x}}=0} \]
Mathematica: cpu = 0.250532 (sec), leaf count = 101 \[ \left \{\left \{y(x)\to \frac {1}{24} \left (24 c_1 x^3-36 c_1 x^2+72 c_1 x-72 c_1 \log (x+1)-36 c_1^2-4 x^6+12 x^5-33 x^4+40 x^3+24 x^3 \log (x+1)-36 x^2-36 x^2 \log (x+1)-36 \log ^2(x+1)+72 x \log (x+1)\right )\right \}\right \} \]
Maple: cpu = 0.234 (sec), leaf count = 37 \[ \left \{ {\it \_C1}-{x}^{3}+{\frac {3\,{x}^{2}}{2}}-3\,x+3\,\ln \left ( 1+x \right ) -{\frac {1}{2}}-\sqrt {{x}^{3}-6\,y \left ( x \right ) }=0 \right \} \]