\[ y'(x)=\frac {y(x) \left (x^3 y(x)+2 x+2\right )}{(x+1) (\log (y(x))+2 x-1)} \] ✓ Mathematica : cpu = 0.733455 (sec), leaf count = 459
\[\left \{\left \{y(x)\to \frac {6 W\left (-\frac {1}{6} \sqrt [6]{e^{-12 x} \left (2 x^3-3 x^2+6 x-6 \log (x+1)+6 c_1\right ){}^6}\right )}{2 x^3-3 x^2+6 x-6 \log (x+1)+6 c_1}\right \},\left \{y(x)\to \frac {6 W\left (\frac {1}{6} \sqrt [6]{e^{-12 x} \left (2 x^3-3 x^2+6 x-6 \log (x+1)+6 c_1\right ){}^6}\right )}{2 x^3-3 x^2+6 x-6 \log (x+1)+6 c_1}\right \},\left \{y(x)\to \frac {6 W\left (-\frac {1}{6} \sqrt [3]{-1} \sqrt [6]{e^{-12 x} \left (2 x^3-3 x^2+6 x-6 \log (x+1)+6 c_1\right ){}^6}\right )}{2 x^3-3 x^2+6 x-6 \log (x+1)+6 c_1}\right \},\left \{y(x)\to \frac {6 W\left (\frac {1}{6} \sqrt [3]{-1} \sqrt [6]{e^{-12 x} \left (2 x^3-3 x^2+6 x-6 \log (x+1)+6 c_1\right ){}^6}\right )}{2 x^3-3 x^2+6 x-6 \log (x+1)+6 c_1}\right \},\left \{y(x)\to \frac {6 W\left (-\frac {1}{6} (-1)^{2/3} \sqrt [6]{e^{-12 x} \left (2 x^3-3 x^2+6 x-6 \log (x+1)+6 c_1\right ){}^6}\right )}{2 x^3-3 x^2+6 x-6 \log (x+1)+6 c_1}\right \},\left \{y(x)\to \frac {6 W\left (\frac {1}{6} (-1)^{2/3} \sqrt [6]{e^{-12 x} \left (2 x^3-3 x^2+6 x-6 \log (x+1)+6 c_1\right ){}^6}\right )}{2 x^3-3 x^2+6 x-6 \log (x+1)+6 c_1}\right \}\right \}\] ✓ Maple : cpu = 0.315 (sec), leaf count = 41
\[y \relax (x ) = {\mathrm e}^{-\LambertW \left (-\frac {\left (-2 x^{3}+3 x^{2}+6 \ln \left (1+x \right )+6 c_{1}-6 x \right ) {\mathrm e}^{-2 x}}{6}\right )-2 x}\]