\[ y'(x)=\frac {2 x y(x)^3+y(x)^3-2 y(x)+6 x y(x) \log ^2(2 x+1)+3 y(x) \log ^2(2 x+1)+6 x y(x)^2 \log (2 x+1)+3 y(x)^2 \log (2 x+1)+2 x \log ^3(2 x+1)+\log ^3(2 x+1)-2 \log (2 x+1)-2}{(2 x+1) (y(x)+\log (2 x+1)+1)} \] ✓ Mathematica : cpu = 0.279504 (sec), leaf count = 124
\[\left \{\left \{y(x)\to \frac {1}{(2 x+1) \left (\frac {2 x+1}{4 x^2+4 x+1}-\frac {1}{(2 x+1) \sqrt {-2 x+c_1}}\right )}-\log (2 x+1)-1\right \},\left \{y(x)\to \frac {1}{(2 x+1) \left (\frac {2 x+1}{4 x^2+4 x+1}+\frac {1}{(2 x+1) \sqrt {-2 x+c_1}}\right )}-\log (2 x+1)-1\right \}\right \}\] ✓ Maple : cpu = 0.08 (sec), leaf count = 79
\[y \relax (x ) = \frac {-\sqrt {c_{1}-2 x}\, \ln \left (2 x +1\right )+\ln \left (2 x +1\right )+1}{\sqrt {c_{1}-2 x}-1}\]