ODE No. 788

$$y^{\prime }(x)=-\frac{y(x)(x^{2}y(x)(-\coth (x+1))+\log (x-1)+x\coth (x+1))}{x\log (x-1)}$$ ✓ Mathematica : cpu = 24.1334 (sec), leaf count = 348

DSolve[Derivative[1][y][x] == -((y[x]*(x*Coth[1 + x] + Log[-1 + x] - x^2*Coth[1 + x]*y[x]))/(x*Log[-1 + x])),y[x],x]
 

$$\left\{\{y(x)\to \frac{\exp ({\int }_1^x\frac{-e^2\cosh (K[1])K[1]-\cosh (K[1])K[1]-e^2\sinh (K[1])K[1]+\sinh (K[1])K[1]-e^2\cosh (K[1])\log (K[1]-1)+\cosh (K[1])\log (K[1]-1)-e^2\log (K[1]-1)\sinh (K[1])-\log (K[1]-1)\sinh (K[1])}{K[1]\log (K[1]-1)(e^2\cosh (K[1])-\cosh (K[1])+e^2\sinh (K[1])+\sinh (K[1]))}dK[1])}{-{\int }_1^x\frac{\exp ({\int }_1^{K[2]}\frac{-e^2\cosh (K[1])K[1]-\cosh (K[1])K[1]-e^2\sinh (K[1])K[1]+\sinh (K[1])K[1]-e^2\cosh (K[1])\log (K[1]-1)+\cosh (K[1])\log (K[1]-1)-e^2\log (K[1]-1)\sinh (K[1])-\log (K[1]-1)\sinh (K[1])}{K[1]\log (K[1]-1)(e^2\cosh (K[1])-\cosh (K[1])+e^2\sinh (K[1])+\sinh (K[1]))}dK[1])(e^2\cosh (K[2])K[2{]}^2+\cosh (K[2])K[2{]}^2+e^2\sinh (K[2])K[2{]}^2-\sinh (K[2])K[2{]}^2)}{K[2]\log (K[2]-1)(e^2\cosh (K[2])-\cosh (K[2])+e^2\sinh (K[2])+\sinh (K[2]))}dK[2]+c_1}\}\right\}$$ ✓ Maple : cpu = 0.355 (sec), leaf count = 108

dsolve(diff(y(x),x) = -y(x)*(ln(x-1)+coth(1+x)*x-coth(1+x)*x^2*y(x))/x/ln(x-1),y(x))
 

$$y\left(x\right)=\frac{{\mathrm{e}}^{\int -\frac{\ln (x-1)\sinh (1+x)+x\cosh (1+x)}{x\ln (x-1)\sinh (1+x)}dx}}{c_1+\int -\frac{{\mathrm{e}}^{\int \frac{-x\cosh (1+x)-\ln (x-1)\sinh (1+x)}{\sinh (1+x)\ln (x-1)x}dx}x\cosh (1+x)}{\ln (x-1)\sinh (1+x)}dx}$$