3.765   ODE No. 765

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

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

Mathematica: cpu = 135.603219 (sec), leaf count = 128 $$\left\{\{y(x)\to \frac{e^{{\text{Li}}_2(-x)+{\text{Li}}_2(x)}{x}^{\log (1-x)-\frac{\log (x)}{2}+\log (x+1)-\log (x-\frac{1}{x})-1}}{c_1-{\int }_1^x\log \left(\frac{(K[1]-1)(K[1]+1)}{K[1]}\right)\exp ({\text{Li}}_2(-K[1])+{\text{Li}}_2(K[1])-\frac{1}{2}\log (K[1])(-2\log (1-K[1])+\log (K[1])-2\log (K[1]+1)+2\log (K[1]-\frac{1}{K[1]})+2))dK[1]}\}\right\}$$

Maple: cpu = 0.110 (sec), leaf count = 106 $$\{y\left(x\right)=\frac{{\mathrm{e}}^{\mathit{d}\mathit{i}\mathit{l}\mathit{o}\mathit{g}(1+x)}{x}^{\ln (1+x)}}{{\mathrm{e}}^{\mathit{d}\mathit{i}\mathit{l}\mathit{o}\mathit{g}\left(x\right)}x}{\mathrm{e}}^{-\frac{{(\ln \left(x\right))}^2}{2}}{(\int -\frac{{\mathrm{e}}^{\mathit{d}\mathit{i}\mathit{l}\mathit{o}\mathit{g}(1+x)}{x}^{\ln (1+x)}}{{\mathrm{e}}^{\mathit{d}\mathit{i}\mathit{l}\mathit{o}\mathit{g}\left(x\right)}x}{\mathrm{e}}^{-\frac{{(\ln \left(x\right))}^2}{2}}\ln \left(\frac{(1+x)(x-1)}{x}\right){\left(x^{\ln \left(\frac{(1+x)(x-1)}{x}\right)}\right)}^{-1}\mathrm{d}x+\mathit{\_}\mathit{C}\mathit{1})}^{-1}{\left(x^{\ln \left(\frac{(1+x)(x-1)}{x}\right)}\right)}^{-1}\}$$