\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac { \left ( 2\,x+2+{x}^{3}y \left ( x \right ) \right ) y \left ( x \right ) }{ \left ( \ln \left ( y \left ( x \right ) \right ) +2\,x-1 \right ) \left ( 1+x \right ) }}=0} \]
Mathematica: cpu = 1.093639 (sec), leaf count = 459 \[ \left \{\left \{y(x)\to \frac {6 W\left (-\frac {1}{6} \sqrt [6]{e^{-12 x} \left (6 c_1+2 x^3-3 x^2+6 x-6 \log (x+1)\right ){}^6}\right )}{6 c_1+2 x^3-3 x^2+6 x-6 \log (x+1)}\right \},\left \{y(x)\to \frac {6 W\left (\frac {1}{6} \sqrt [6]{e^{-12 x} \left (6 c_1+2 x^3-3 x^2+6 x-6 \log (x+1)\right ){}^6}\right )}{6 c_1+2 x^3-3 x^2+6 x-6 \log (x+1)}\right \},\left \{y(x)\to \frac {6 W\left (-\frac {1}{6} \sqrt [3]{-1} \sqrt [6]{e^{-12 x} \left (6 c_1+2 x^3-3 x^2+6 x-6 \log (x+1)\right ){}^6}\right )}{6 c_1+2 x^3-3 x^2+6 x-6 \log (x+1)}\right \},\left \{y(x)\to \frac {6 W\left (\frac {1}{6} \sqrt [3]{-1} \sqrt [6]{e^{-12 x} \left (6 c_1+2 x^3-3 x^2+6 x-6 \log (x+1)\right ){}^6}\right )}{6 c_1+2 x^3-3 x^2+6 x-6 \log (x+1)}\right \},\left \{y(x)\to \frac {6 W\left (-\frac {1}{6} (-1)^{2/3} \sqrt [6]{e^{-12 x} \left (6 c_1+2 x^3-3 x^2+6 x-6 \log (x+1)\right ){}^6}\right )}{6 c_1+2 x^3-3 x^2+6 x-6 \log (x+1)}\right \},\left \{y(x)\to \frac {6 W\left (\frac {1}{6} (-1)^{2/3} \sqrt [6]{e^{-12 x} \left (6 c_1+2 x^3-3 x^2+6 x-6 \log (x+1)\right ){}^6}\right )}{6 c_1+2 x^3-3 x^2+6 x-6 \log (x+1)}\right \}\right \} \]
Maple: cpu = 0.187 (sec), leaf count = 41 \[ \left \{ y \left ( x \right ) ={{\rm e}^{-{\it lambertW} \left ( -{\frac { \left ( -2\,{x}^{3}+3\,{x}^{2}+6\,\ln \left ( 1+x \right ) +6\,{\it \_C1}-6\,x \right ) {{\rm e}^{-2\,x}}}{6}} \right ) -2\,x}} \right \} \]