ODE No. 871

$$y^{\prime }(x)=\frac{2xy(x{)}^2+y(x{)}^2+4xy(x)\log (2x+1)+2y(x)\log (2x+1)+2x{\log }^2(2x+1)+{\log }^2(2x+1)-2}{2x+1}$$ ✓ 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]
 

$$\left\{\{y(x)\to -\log (2x+1)+\frac{1}{-x+c_1}\}\right\}$$ ✓ 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))
 

$$y\left(x\right)=\frac{-1+(c_1-x)\ln (2x+1)}{-c_1+x}$$