2.788   ODE No. 788

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

$$y^{\prime }(x)=-\frac{y(x)(x^{2}y(x)(-\coth (x+1))+\log (x-1)+x\coth (x+1))}{x\log (x-1)}$$ ✓ Mathematica : cpu = 24.8381 (sec), leaf count = 348

$$\left\{\{y(x)\to \frac{\exp ({\int }_1^x\frac{-e^2\cosh (K[1])K[1]-\cosh (K[1])K[1]-e^2\sinh (K[1])K[1]+\sinh (K[1])K[1]-e^2\cosh (K[1])\log (K[1]-1)+\cosh (K[1])\log (K[1]-1)-e^2\log (K[1]-1)\sinh (K[1])-\log (K[1]-1)\sinh (K[1])}{K[1]\log (K[1]-1)(e^2\cosh (K[1])-\cosh (K[1])+e^2\sinh (K[1])+\sinh (K[1]))}dK[1])}{-{\int }_1^x\frac{\exp ({\int }_1^{K[2]}\frac{-e^2\cosh (K[1])K[1]-\cosh (K[1])K[1]-e^2\sinh (K[1])K[1]+\sinh (K[1])K[1]-e^2\cosh (K[1])\log (K[1]-1)+\cosh (K[1])\log (K[1]-1)-e^2\log (K[1]-1)\sinh (K[1])-\log (K[1]-1)\sinh (K[1])}{K[1]\log (K[1]-1)(e^2\cosh (K[1])-\cosh (K[1])+e^2\sinh (K[1])+\sinh (K[1]))}dK[1])(e^2\cosh (K[2])K[2{]}^2+\cosh (K[2])K[2{]}^2+e^2\sinh (K[2])K[2{]}^2-\sinh (K[2])K[2{]}^2)}{K[2]\log (K[2]-1)(e^2\cosh (K[2])-\cosh (K[2])+e^2\sinh (K[2])+\sinh (K[2]))}dK[2]+c_1}\}\right\}$$ ✓ Maple : cpu = 0.279 (sec), leaf count = 108

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