\[ y'(x)=\frac {y(x) \left (x^2 y(x) \log \left (\frac {x^2+1}{x}\right )-x \log \left (\frac {x^2+1}{x}\right )-\log \left (\frac {1}{x}\right )\right )}{x \log \left (\frac {1}{x}\right )} \] ✓ Mathematica : cpu = 0.378235 (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 = 0.246 (sec), leaf count = 96
\[y \relax (x ) = \frac {{\mathrm e}^{\int \frac {-\ln \left (\frac {x^{2}+1}{x}\right ) x -\ln \left (\frac {1}{x}\right )}{x \ln \left (\frac {1}{x}\right )}d x}}{\int -\frac {{\mathrm e}^{\int \frac {-\ln \left (\frac {x^{2}+1}{x}\right ) x -\ln \left (\frac {1}{x}\right )}{x \ln \left (\frac {1}{x}\right )}d x} \ln \left (\frac {x^{2}+1}{x}\right ) x}{\ln \left (\frac {1}{x}\right )}d x +c_{1}}\]