\[ y'(x)=\frac {x^3 \left (\sqrt {9 x^4-4 y(x)^3}+3 x+3\right )}{(x+1) y(x)^2} \] ✓ Mathematica : cpu = 4.36012 (sec), leaf count = 272
\[\left \{\left \{y(x)\to \sqrt [3]{\left (6 c_1+9\right ) x^3-9 \left (c_1+1\right ) x^2+3 \left (-6 c_1+2 x^3-3 x^2+6 x\right ) \log (x+1)+18 c_1 x-9 c_1^2-x^6+3 x^5-6 x^4-9 \log ^2(x+1)}\right \},\left \{y(x)\to -\sqrt [3]{-1} \sqrt [3]{\left (6 c_1+9\right ) x^3-9 \left (c_1+1\right ) x^2+3 \left (-6 c_1+2 x^3-3 x^2+6 x\right ) \log (x+1)+18 c_1 x-9 c_1^2-x^6+3 x^5-6 x^4-9 \log ^2(x+1)}\right \},\left \{y(x)\to (-1)^{2/3} \sqrt [3]{\left (6 c_1+9\right ) x^3-9 \left (c_1+1\right ) x^2+3 \left (-6 c_1+2 x^3-3 x^2+6 x\right ) \log (x+1)+18 c_1 x-9 c_1^2-x^6+3 x^5-6 x^4-9 \log ^2(x+1)}\right \}\right \}\]
✓ Maple : cpu = 0.244 (sec), leaf count = 48
\[ \left \{ \int _{{\it \_b}}^{y \left ( x \right ) }\!{{{\it \_a}}^{2}{\frac {1}{\sqrt {9\,{x}^{4}-4\,{{\it \_a}}^{3}}}}}\,{\rm d}{\it \_a}-{\frac {{x}^{3}}{3}}+{\frac {{x}^{2}}{2}}-x+\ln \left ( 1+x \right ) -{\it \_C1}=0 \right \} \]