\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =-1/3\,{\frac {2\,{x}^{2}+2\,x-3\,\sqrt {{x}^{2}+3\,y \left ( x \right ) }}{1+x}}=0} \]
Mathematica: cpu = 0.165021 (sec), leaf count = 37 \[ \left \{\left \{y(x)\to \frac {1}{12} \left (-18 c_1 \log (x+1)+9 c_1^2-4 x^2+9 \log ^2(x+1)\right )\right \}\right \} \]
Maple: cpu = 0.203 (sec), leaf count = 23 \[ \left \{ {\it \_C1}+{\frac {3\,\ln \left ( 1+x \right ) }{2}}-\sqrt {{x }^{2}+3\,y \left ( x \right ) }=0 \right \} \]