#### 2.788   ODE No. 788

$y'(x)=-\frac {y(x) \left (x^2 y(x) (-\coth (x+1))+\log (x-1)+x \coth (x+1)\right )}{x \log (x-1)}$ Mathematica : cpu = 28.5492 (sec), leaf count = 348

$\left \{\left \{y(x)\to \frac {\exp \left (\int _1^x\frac {-e^2 \cosh (K[1]) K[1]-\cosh (K[1]) K[1]-e^2 \sinh (K[1]) K[1]+\sinh (K[1]) K[1]-e^2 \cosh (K[1]) \log (K[1]-1)+\cosh (K[1]) \log (K[1]-1)-e^2 \log (K[1]-1) \sinh (K[1])-\log (K[1]-1) \sinh (K[1])}{K[1] \log (K[1]-1) \left (e^2 \cosh (K[1])-\cosh (K[1])+e^2 \sinh (K[1])+\sinh (K[1])\right )}dK[1]\right )}{c_1-\int _1^x\frac {\exp \left (\int _1^{K[2]}\frac {-e^2 \cosh (K[1]) K[1]-\cosh (K[1]) K[1]-e^2 \sinh (K[1]) K[1]+\sinh (K[1]) K[1]-e^2 \cosh (K[1]) \log (K[1]-1)+\cosh (K[1]) \log (K[1]-1)-e^2 \log (K[1]-1) \sinh (K[1])-\log (K[1]-1) \sinh (K[1])}{K[1] \log (K[1]-1) \left (e^2 \cosh (K[1])-\cosh (K[1])+e^2 \sinh (K[1])+\sinh (K[1])\right )}dK[1]\right ) \left (e^2 \cosh (K[2]) K[2]^2+\cosh (K[2]) K[2]^2+e^2 \sinh (K[2]) K[2]^2-\sinh (K[2]) K[2]^2\right )}{K[2] \log (K[2]-1) \left (e^2 \cosh (K[2])-\cosh (K[2])+e^2 \sinh (K[2])+\sinh (K[2])\right )}dK[2]}\right \}\right \}$ Maple : cpu = 0.166 (sec), leaf count = 108

$\left \{ y \left ( x \right ) ={1 \left ( {{\rm e}^{-\int \!{\frac {-\ln \left ( x-1 \right ) \sinh \left ( 1+x \right ) -x\cosh \left ( 1+x \right ) }{\sinh \left ( 1+x \right ) x\ln \left ( x-1 \right ) }}\,{\rm d}x}} \right ) ^{-1} \left ( {\it \_C1}+\int \!-{\frac {x\cosh \left ( 1+x \right ) }{\ln \left ( x-1 \right ) \sinh \left ( 1+x \right ) }{{\rm e}^{\int \!{\frac {-\ln \left ( x-1 \right ) \sinh \left ( 1+x \right ) -x\cosh \left ( 1+x \right ) }{\sinh \left ( 1+x \right ) x\ln \left ( x-1 \right ) }}\,{\rm d}x}}}\,{\rm d}x \right ) ^{-1}} \right \}$