\[ y'(x)=\frac {y(x) \left (x^2 y(x) \log \left (\frac {x^2+1}{x}\right )-x \log \left (\frac {x^2+1}{x}\right )-\log \left (\frac {1}{x}\right )\right )}{x \log \left (\frac {1}{x}\right )} \] ✗ Mathematica : cpu = 300.046 (sec), leaf count = 0 , timed out
$Aborted
✓ Maple : cpu = 0.228 (sec), leaf count = 96
\[ \left \{ y \left ( x \right ) ={1{{\rm e}^{\int \!{\frac {1}{x\ln \left ( {x}^{-1} \right ) } \left ( -\ln \left ( {\frac {{x}^{2}+1}{x}} \right ) x-\ln \left ( {x}^{-1} \right ) \right ) }\,{\rm d}x}} \left ( \int \!-{\frac {x}{\ln \left ( {x}^{-1} \right ) }{{\rm e}^{\int \!{\frac {1}{x\ln \left ( {x}^{-1} \right ) } \left ( -\ln \left ( {\frac {{x}^{2}+1}{x}} \right ) x-\ln \left ( {x}^{-1} \right ) \right ) }\,{\rm d}x}}\ln \left ( {\frac {{x}^{2}+1}{x}} \right ) }\,{\rm d}x+{\it \_C1} \right ) ^{-1}} \right \} \]