\[ y'(x)=\frac {\sqrt {9 x^4-4 y(x)^3}+3 x^4+3 x^3}{(x+1) y(x)^2} \] ✓ Mathematica : cpu = 6.28473 (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 = 0.354 (sec), leaf count = 37
\[ \left \{ \int _{{\it \_b}}^{y \left ( x \right ) }\!{{{\it \_a}}^{2}{\frac {1}{\sqrt {9\,{x}^{4}-4\,{{\it \_a}}^{3}}}}}\,{\rm d}{\it \_a}-\ln \left ( 1+x \right ) -{\it \_C1}=0 \right \} \]