\[ y'(x)=\frac {x^3 \left (\sqrt {9 x^4-4 y(x)^3}+3 x+3\right )}{(x+1) y(x)^2} \] ✓ Mathematica : cpu = 2.93465 (sec), leaf count = 314
\[\left \{\left \{y(x)\to \sqrt [3]{-x^6+3 x^5-6 x^4+9 x^3-9 x^2+6 x^3 \log (x+1)-9 x^2 \log (x+1)+6 c_1 x^3-9 c_1 x^2-9 \log ^2(x+1)+18 x \log (x+1)+18 c_1 x-18 c_1 \log (x+1)-9 c_1{}^2}\right \},\left \{y(x)\to -\sqrt [3]{-1} \sqrt [3]{-x^6+3 x^5-6 x^4+9 x^3-9 x^2+6 x^3 \log (x+1)-9 x^2 \log (x+1)+6 c_1 x^3-9 c_1 x^2-9 \log ^2(x+1)+18 x \log (x+1)+18 c_1 x-18 c_1 \log (x+1)-9 c_1{}^2}\right \},\left \{y(x)\to (-1)^{2/3} \sqrt [3]{-x^6+3 x^5-6 x^4+9 x^3-9 x^2+6 x^3 \log (x+1)-9 x^2 \log (x+1)+6 c_1 x^3-9 c_1 x^2-9 \log ^2(x+1)+18 x \log (x+1)+18 c_1 x-18 c_1 \log (x+1)-9 c_1{}^2}\right \}\right \}\] ✓ Maple : cpu = 0.264 (sec), leaf count = 48
\[ \left \{ \int _{{\it \_b}}^{y \left ( x \right ) }\!{{{\it \_a}}^{2}{\frac {1}{\sqrt {9\,{x}^{4}-4\,{{\it \_a}}^{3}}}}}\,{\rm d}{\it \_a}-{\frac {{x}^{3}}{3}}+{\frac {{x}^{2}}{2}}-x+\ln \left ( 1+x \right ) -{\it \_C1}=0 \right \} \]