\[ y'(x)=\frac {x^3 \left (\sqrt {9 x^4-4 y(x)^3}+3 x+3\right )}{(x+1) y(x)^2} \] ✓ Mathematica : cpu = 2.51908 (sec), leaf count = 314
\[\left \{\left \{y(x)\to \sqrt [3]{-x^6+3 x^5-6 x^4+9 x^3+6 x^3 \log (x+1)+6 c_1 x^3-9 x^2-9 x^2 \log (x+1)-9 c_1 x^2-9 \log ^2(x+1)+18 x \log (x+1)+18 c_1 x-18 c_1 \log (x+1)-9 c_1{}^2}\right \},\left \{y(x)\to -\sqrt [3]{-1} \sqrt [3]{-x^6+3 x^5-6 x^4+9 x^3+6 x^3 \log (x+1)+6 c_1 x^3-9 x^2-9 x^2 \log (x+1)-9 c_1 x^2-9 \log ^2(x+1)+18 x \log (x+1)+18 c_1 x-18 c_1 \log (x+1)-9 c_1{}^2}\right \},\left \{y(x)\to (-1)^{2/3} \sqrt [3]{-x^6+3 x^5-6 x^4+9 x^3+6 x^3 \log (x+1)+6 c_1 x^3-9 x^2-9 x^2 \log (x+1)-9 c_1 x^2-9 \log ^2(x+1)+18 x \log (x+1)+18 c_1 x-18 c_1 \log (x+1)-9 c_1{}^2}\right \}\right \}\] ✓ Maple : cpu = 0.212 (sec), leaf count = 48
\[\int _{\textit {\_b}}^{y \relax (x )}\frac {\textit {\_a}^{2}}{\sqrt {9 x^{4}-4 \textit {\_a}^{3}}}d \textit {\_a} -\frac {x^{3}}{3}+\frac {x^{2}}{2}-x +\ln \left (1+x \right )-c_{1} = 0\]