3.871   ODE No. 871

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=\frac{2x{\left(y\left(x\right)\right)}^2+4y\left(x\right)\ln (2x+1)x+2{(\ln (2x+1))}^{2}x+{\left(y\left(x\right)\right)}^2-2+{(\ln (2x+1))}^2+2y\left(x\right)\ln (2x+1)}{2x+1}=0}}$$

1. Problem in Latex
2. Mathematica input
3. Maple input

Mathematica: cpu = 0.022503 (sec), leaf count = 22 $$\left\{\{y(x)\to \frac{1}{c_1-x}-\log (2x+1)\}\right\}$$

Maple: cpu = 0.062 (sec), leaf count = 66 $$\{y\left(x\right)=-\frac{1}{2}(4\frac{\ln (2x+1)x}{2x+1}+2\frac{\ln (2x+1)}{2x+1}){(2\frac{x}{2x+1}+{(2x+1)}^{-1})}^{-1}+{(\mathit{\_}\mathit{C}\mathit{1}-x)}^{-1}\}$$