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