\[ y'(x)=\frac {2 x y(x)^3+y(x)^3+2 x y(x)^2+y(x)^2+6 x y(x) \log ^2(2 x+1)+3 y(x) \log ^2(2 x+1)+6 x y(x)^2 \log (2 x+1)+3 y(x)^2 \log (2 x+1)+4 x y(x) \log (2 x+1)+2 y(x) \log (2 x+1)+2 x+2 x \log ^3(2 x+1)+\log ^3(2 x+1)+2 x \log ^2(2 x+1)+\log ^2(2 x+1)-1}{2 x+1} \] ✓ Mathematica : cpu = 0.409979 (sec), leaf count = 82
DSolve[Derivative[1][y][x] == (-1 + 2*x + Log[1 + 2*x]^2 + 2*x*Log[1 + 2*x]^2 + Log[1 + 2*x]^3 + 2*x*Log[1 + 2*x]^3 + 2*Log[1 + 2*x]*y[x] + 4*x*Log[1 + 2*x]*y[x] + 3*Log[1 + 2*x]^2*y[x] + 6*x*Log[1 + 2*x]^2*y[x] + y[x]^2 + 2*x*y[x]^2 + 3*Log[1 + 2*x]*y[x]^2 + 6*x*Log[1 + 2*x]*y[x]^2 + y[x]^3 + 2*x*y[x]^3)/(1 + 2*x),y[x],x]
\[\text {Solve}\left [-\frac {29}{3} \text {RootSum}\left [-29 \text {$\#$1}^3+3 \sqrt [3]{29} \text {$\#$1}-29\& ,\frac {\log \left (\frac {3 y(x)+3 \log (2 x+1)+1}{\sqrt [3]{29}}-\text {$\#$1}\right )}{\sqrt [3]{29}-29 \text {$\#$1}^2}\& \right ]=\frac {1}{9} 29^{2/3} x+c_1,y(x)\right ]\] ✓ Maple : cpu = 0.062 (sec), leaf count = 40
dsolve(diff(y(x),x) = 1/(2*x+1)*(2*x+4*y(x)*ln(2*x+1)*x+6*y(x)^2*ln(2*x+1)*x+6*y(x)*ln(2*x+1)^2*x+2*ln(2*x+1)^3*x+2*x*y(x)^3+2*ln(2*x+1)^2*x+2*x*y(x)^2-1+3*y(x)^2*ln(2*x+1)+3*y(x)*ln(2*x+1)^2+y(x)^2+y(x)^3+2*y(x)*ln(2*x+1)+ln(2*x+1)^2+ln(2*x+1)^3),y(x))
\[y \left (x \right ) = -\ln \left (2 x +1\right )-\frac {1}{3}+\frac {29 \RootOf \left (-81 \left (\int _{}^{\textit {\_Z}}\frac {1}{841 \textit {\_a}^{3}-27 \textit {\_a} +27}d \textit {\_a} \right )+x +3 c_{1}\right )}{9}\]