\[ y'(x)=\frac {2 x y(x)^3+y(x)^3-2 y(x)+6 x y(x) \log ^2(2 x+1)+3 y(x) \log ^2(2 x+1)+6 x y(x)^2 \log (2 x+1)+3 y(x)^2 \log (2 x+1)+2 x \log ^3(2 x+1)+\log ^3(2 x+1)-2 \log (2 x+1)-2}{(2 x+1) (y(x)+\log (2 x+1)+1)} \] ✓ Mathematica : cpu = 0.0274723 (sec), leaf count = 83
\[\left \{\left \{y(x)\to \frac {1-\left (\sqrt {c_1-2 x}-1\right ) \log (2 x+1)}{\sqrt {c_1-2 x}-1}\right \},\left \{y(x)\to -\frac {\left (\sqrt {c_1-2 x}+1\right ) \log (2 x+1)+1}{\sqrt {c_1-2 x}+1}\right \}\right \}\]
✓ Maple : cpu = 0.066 (sec), leaf count = 79
\[ \left \{ y \left ( x \right ) ={1 \left ( -\sqrt {{\it \_C1}-2\,x}\ln \left ( 2\,x+1 \right ) -\ln \left ( 2\,x+1 \right ) -1 \right ) \left ( \sqrt {{\it \_C1}-2\,x}+1 \right ) ^{-1}},y \left ( x \right ) ={1 \left ( -\sqrt {{\it \_C1}-2\,x}\ln \left ( 2\,x+1 \right ) +\ln \left ( 2\,x+1 \right ) +1 \right ) \left ( \sqrt {{\it \_C1}-2\,x}-1 \right ) ^{-1}} \right \} \]