#### 2.776   ODE No. 776

$y'(x)=\frac {y(x) \left (x^2 y(x) \log \left (\frac {x^2+1}{x}\right )-x \log \left (\frac {x^2+1}{x}\right )-\log \left (\frac {1}{x}\right )\right )}{x \log \left (\frac {1}{x}\right )}$ Mathematica : cpu = 0.367995 (sec), leaf count = 133

$\left \{\left \{y(x)\to \frac {\exp \left (\int _1^x\frac {-\log \left (\frac {1}{K[1]}\right )-K[1] \log \left (\frac {K[1]^2+1}{K[1]}\right )}{K[1] \log \left (\frac {1}{K[1]}\right )}dK[1]\right )}{-\int _1^x\frac {\exp \left (\int _1^{K[2]}\frac {-\log \left (\frac {1}{K[1]}\right )-K[1] \log \left (\frac {K[1]^2+1}{K[1]}\right )}{K[1] \log \left (\frac {1}{K[1]}\right )}dK[1]\right ) K[2] \log \left (\frac {K[2]^2+1}{K[2]}\right )}{\log \left (\frac {1}{K[2]}\right )}dK[2]+c_1}\right \}\right \}$ Maple : cpu = 0.294 (sec), leaf count = 96

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