\[ y'(x)=\frac {y(x) \left (x^3 y(x)+2 x+2\right )}{(x+1) (\log (y(x))+2 x-1)} \] ✓ Mathematica : cpu = 0.775661 (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 = 0.385 (sec), leaf count = 41
\[ \left \{ y \left ( x \right ) ={{\rm e}^{-{\it lambertW} \left ( -{\frac { \left ( -2\,{x}^{3}+3\,{x}^{2}+6\,\ln \left ( 1+x \right ) +6\,{\it \_C1}-6\,x \right ) {{\rm e}^{-2\,x}}}{6}} \right ) -2\,x}} \right \} \]