2.766   ODE No. 766

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

$$y^{\prime }(x)=\frac{y(x)(x^{2}y(x)\log \left(\frac{(x-1)(x+1)}{x}\right)-x\log \left(\frac{(x-1)(x+1)}{x}\right)-\log (x))}{x\log (x)}$$ ✓ Mathematica : cpu = 0.307829 (sec), leaf count = 129

$$\left\{\{y(x)\to \frac{\exp ({\int }_1^x\frac{-\log (K[1])-K[1]\log \left(\frac{(K[1]-1)(K[1]+1)}{K[1]}\right)}{K[1]\log (K[1])}dK[1])}{-{\int }_1^x\frac{\exp ({\int }_1^{K[2]}\frac{-\log (K[1])-K[1]\log \left(\frac{(K[1]-1)(K[1]+1)}{K[1]}\right)}{K[1]\log (K[1])}dK[1])K[2]\log \left(\frac{(K[2]-1)(K[2]+1)}{K[2]}\right)}{\log (K[2])}dK[2]+c_1}\}\right\}$$ ✓ Maple : cpu = 0.327 (sec), leaf count = 89

$$\{y\left(x\right)={\mathrm{e}}^{\int \frac{1}{x\ln \left(x\right)}(-x\ln \left(\frac{(1+x)(x-1)}{x}\right)-\ln \left(x\right))\mathrm{d}x}{(\int -\frac{x}{\ln \left(x\right)}{\mathrm{e}}^{\int \frac{1}{x\ln \left(x\right)}(-x\ln \left(\frac{(1+x)(x-1)}{x}\right)-\ln \left(x\right))\mathrm{d}x}\ln \left(\frac{(1+x)(x-1)}{x}\right)\mathrm{d}x+\mathit{\_}\mathit{C}\mathit{1})}^{-1}\}$$