\[ y'(x)=\frac {\sqrt {9 x^4-4 y(x)^3}+3 x^4+3 x^3}{(x+1) y(x)^2} \] ✓ Mathematica : cpu = 2.36111 (sec), leaf count = 133
\[\left \{\left \{y(x)\to \left (-\frac {3}{2}\right )^{2/3} \sqrt [3]{x^4-4 \log ^2(x+1)+8 c_1 \log (x+1)-4 c_1{}^2}\right \},\left \{y(x)\to \left (\frac {3}{2}\right )^{2/3} \sqrt [3]{x^4-4 \log ^2(x+1)+8 c_1 \log (x+1)-4 c_1{}^2}\right \},\left \{y(x)\to -\sqrt [3]{-1} \left (\frac {3}{2}\right )^{2/3} \sqrt [3]{x^4-4 \log ^2(x+1)+8 c_1 \log (x+1)-4 c_1{}^2}\right \}\right \}\] ✓ Maple : cpu = 0.312 (sec), leaf count = 37
\[\int _{\textit {\_b}}^{y \relax (x )}\frac {\textit {\_a}^{2}}{\sqrt {9 x^{4}-4 \textit {\_a}^{3}}}d \textit {\_a} -\ln \left (1+x \right )-c_{1} = 0\]