\[ y'(x)=\frac {2 x y(x)^2+y(x)^2+4 x y(x) \log (2 x+1)+2 y(x) \log (2 x+1)+2 x \log ^2(2 x+1)+\log ^2(2 x+1)-2}{2 x+1} \] ✓ Mathematica : cpu = 0.301742 (sec), leaf count = 22
\[\left \{\left \{y(x)\to -\log (2 x+1)+\frac {1}{-x+c_1}\right \}\right \}\] ✓ Maple : cpu = 0.09 (sec), leaf count = 26
\[y \relax (x ) = \frac {-1+\left (c_{1}-x \right ) \ln \left (2 x +1\right )}{-c_{1}+x}\]