\[ y'(x)=-\frac {y(x) \left (x^2 y(x) (-\coth (x+1))+\log (x-1)+x \coth (x+1)\right )}{x \log (x-1)} \] ✓ Mathematica : cpu = 24.1334 (sec), leaf count = 348
\[\left \{\left \{y(x)\to \frac {\exp \left (\int _1^x\frac {-e^2 \cosh (K[1]) K[1]-\cosh (K[1]) K[1]-e^2 \sinh (K[1]) K[1]+\sinh (K[1]) K[1]-e^2 \cosh (K[1]) \log (K[1]-1)+\cosh (K[1]) \log (K[1]-1)-e^2 \log (K[1]-1) \sinh (K[1])-\log (K[1]-1) \sinh (K[1])}{K[1] \log (K[1]-1) \left (e^2 \cosh (K[1])-\cosh (K[1])+e^2 \sinh (K[1])+\sinh (K[1])\right )}dK[1]\right )}{-\int _1^x\frac {\exp \left (\int _1^{K[2]}\frac {-e^2 \cosh (K[1]) K[1]-\cosh (K[1]) K[1]-e^2 \sinh (K[1]) K[1]+\sinh (K[1]) K[1]-e^2 \cosh (K[1]) \log (K[1]-1)+\cosh (K[1]) \log (K[1]-1)-e^2 \log (K[1]-1) \sinh (K[1])-\log (K[1]-1) \sinh (K[1])}{K[1] \log (K[1]-1) \left (e^2 \cosh (K[1])-\cosh (K[1])+e^2 \sinh (K[1])+\sinh (K[1])\right )}dK[1]\right ) \left (e^2 \cosh (K[2]) K[2]^2+\cosh (K[2]) K[2]^2+e^2 \sinh (K[2]) K[2]^2-\sinh (K[2]) K[2]^2\right )}{K[2] \log (K[2]-1) \left (e^2 \cosh (K[2])-\cosh (K[2])+e^2 \sinh (K[2])+\sinh (K[2])\right )}dK[2]+c_1}\right \}\right \}\] ✓ Maple : cpu = 0.355 (sec), leaf count = 108
\[y \relax (x ) = \frac {{\mathrm e}^{\int -\frac {\ln \left (x -1\right ) \sinh \left (1+x \right )+x \cosh \left (1+x \right )}{x \ln \left (x -1\right ) \sinh \left (1+x \right )}d x}}{c_{1}+\int -\frac {{\mathrm e}^{\int \frac {-x \cosh \left (1+x \right )-\ln \left (x -1\right ) \sinh \left (1+x \right )}{\sinh \left (1+x \right ) \ln \left (x -1\right ) x}d x} x \cosh \left (1+x \right )}{\ln \left (x -1\right ) \sinh \left (1+x \right )}d x}\]