\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {3\,{x}^{4}+3\,{x}^{3}+\sqrt {9\,{x}^{4}-4\, \left ( y \left ( x \right ) \right ) ^{3}}}{ \left ( 1+x \right ) \left ( y \left ( x \right ) \right ) ^{2}}}=0} \]
Mathematica: cpu = 5.769733 (sec), leaf count = 133 \[ \left \{\left \{y(x)\to \left (-\frac {3}{2}\right )^{2/3} \sqrt [3]{8 c_1 \log (x+1)-4 c_1^2+x^4-4 \log ^2(x+1)}\right \},\left \{y(x)\to \left (\frac {3}{2}\right )^{2/3} \sqrt [3]{8 c_1 \log (x+1)-4 c_1^2+x^4-4 \log ^2(x+1)}\right \},\left \{y(x)\to -\sqrt [3]{-1} \left (\frac {3}{2}\right )^{2/3} \sqrt [3]{8 c_1 \log (x+1)-4 c_1^2+x^4-4 \log ^2(x+1)}\right \}\right \} \]
Maple: cpu = 0.249 (sec), leaf count = 37 \[ \left \{ \int _{{\it \_b}}^{y \left ( x \right ) }\!{{{\it \_a}}^{2}{ \frac {1}{\sqrt {9\,{x}^{4}-4\,{{\it \_a}}^{3}}}}}\,{\rm d}{\it \_a}- \ln \left ( 1+x \right ) -{\it \_C1}=0 \right \} \]