2.782   ODE No. 782

$y'(x)=\frac {y(x) \coth \left (\frac {1}{x}\right ) \left (x^2 y(x) \log \left (\frac {x^2+1}{x}\right )-x \log \left (\frac {x^2+1}{x}\right )-\tanh \left (\frac {1}{x}\right )\right )}{x}$ Mathematica : cpu = 3.95979 (sec), leaf count = 115

$\left \{\left \{y(x)\to \frac {\exp \left (\int _1^x\frac {-\coth \left (\frac {1}{K[1]}\right ) K[1] \log \left (\frac {K[1]^2+1}{K[1]}\right )-1}{K[1]}dK[1]\right )}{-\int _1^x\exp \left (\int _1^{K[2]}\frac {-\coth \left (\frac {1}{K[1]}\right ) K[1] \log \left (\frac {K[1]^2+1}{K[1]}\right )-1}{K[1]}dK[1]\right ) \coth \left (\frac {1}{K[2]}\right ) K[2] \log \left (\frac {K[2]^2+1}{K[2]}\right )dK[2]+c_1}\right \}\right \}$ Maple : cpu = 2.435 (sec), leaf count = 96

$\left \{ y \left ( x \right ) ={{{\rm e}^{\int \!{\frac {1}{x\tanh \left ( {x}^{-1} \right ) } \left ( -\ln \left ( {\frac {{x}^{2}+1}{x}} \right ) x-\tanh \left ( {x}^{-1} \right ) \right ) }\,{\rm d}x}} \left ( \int \!-{\frac {x}{\tanh \left ( {x}^{-1} \right ) }{{\rm e}^{\int \!{\frac {1}{x\tanh \left ( {x}^{-1} \right ) } \left ( -\ln \left ( {\frac {{x}^{2}+1}{x}} \right ) x-\tanh \left ( {x}^{-1} \right ) \right ) }\,{\rm d}x}}\ln \left ( {\frac {{x}^{2}+1}{x}} \right ) }\,{\rm d}x+{\it \_C1} \right ) ^{-1}} \right \}$