\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) =1/3\,{\frac {x \left ( -2\,x-2+3\,{x}^{2}\sqrt {{x}^{2}+3\,y \left ( x \right ) } \right ) }{1+x}}=0} \]
Mathematica: cpu = 0.243531 (sec), leaf count = 101 \[ \left \{\left \{y(x)\to \frac {1}{48} \left (-24 c_1 x^3+36 c_1 x^2-72 c_1 x+72 c_1 \log (x+1)+36 c_1^2+4 x^6-12 x^5+33 x^4-36 x^3-24 x^3 \log (x+1)+20 x^2+36 x^2 \log (x+1)+36 \log ^2(x+1)-72 x \log (x+1)\right )\right \}\right \} \]
Maple: cpu = 0.265 (sec), leaf count = 36 \[ \left \{ {\it \_C1}+{\frac {{x}^{3}}{2}}-{\frac {3\,{x}^{2}}{4}}+{ \frac {3\,x}{2}}-{\frac {3\,\ln \left ( 1+x \right ) }{2}}-\sqrt {{x}^{ 2}+3\,y \left ( x \right ) }=0 \right \} \]