3.687   ODE No. 687

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=\frac{1}{x}(y\left(x\right)-\ln \left(\frac{1+x}{x-1}\right)x^3+\ln \left(\frac{1+x}{x-1}\right)x{\left(y\left(x\right)\right)}^2)=0}}$$

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

Mathematica: cpu = 0.064008 (sec), leaf count = 130 $$\left\{\{y(x)\to \frac{-x^2(x+1{)}^{x^2}{e}^{2c_1+2x}+x(x+1{)}^{x^2}{e}^{2c_1+2x}-x^2(x-1{)}^{x^2}-x(x-1{)}^{x^2}}{-(x+1{)}^{x^2}{e}^{2c_1+2x}+x(x+1{)}^{x^2}{e}^{2c_1+2x}-x(x-1{)}^{x^2}-(x-1{)}^{x^2}}\}\right\}$$

Maple: cpu = 0.063 (sec), leaf count = 39 $$\{y\left(x\right)=-\tanh (\frac{x^2}{2}\ln \left(\frac{1+x}{x-1}\right)-\frac{1}{2}\ln \left(\frac{1+x}{x-1}\right)+\mathit{\_}\mathit{C}\mathit{1}+x-1)x\}$$