\[ y'(x)=\frac {y(x) \coth \left (\frac {1}{x}\right ) \left (x^2 y(x) \log \left (\frac {x^2+1}{x}\right )-x \log \left (\frac {x^2+1}{x}\right )-\tanh \left (\frac {1}{x}\right )\right )}{x} \] ✓ Mathematica : cpu = 4.03079 (sec), leaf count = 115
DSolve[Derivative[1][y][x] == (Coth[x^(-1)]*y[x]*(-(x*Log[(1 + x^2)/x]) - Tanh[x^(-1)] + x^2*Log[(1 + x^2)/x]*y[x]))/x,y[x],x]
\[\left \{\left \{y(x)\to \frac {\exp \left (\int _1^x\frac {-\coth \left (\frac {1}{K[1]}\right ) K[1] \log \left (\frac {K[1]^2+1}{K[1]}\right )-1}{K[1]}dK[1]\right )}{-\int _1^x\exp \left (\int _1^{K[2]}\frac {-\coth \left (\frac {1}{K[1]}\right ) K[1] \log \left (\frac {K[1]^2+1}{K[1]}\right )-1}{K[1]}dK[1]\right ) \coth \left (\frac {1}{K[2]}\right ) K[2] \log \left (\frac {K[2]^2+1}{K[2]}\right )dK[2]+c_1}\right \}\right \}\] ✓ Maple : cpu = 1.714 (sec), leaf count = 96
dsolve(diff(y(x),x) = y(x)*(-tanh(1/x)-ln((x^2+1)/x)*x+ln((x^2+1)/x)*x^2*y(x))/x/tanh(1/x),y(x))
\[y \left (x \right ) = \frac {{\mathrm e}^{\int \frac {-\ln \left (\frac {x^{2}+1}{x}\right ) x -\tanh \left (\frac {1}{x}\right )}{x \tanh \left (\frac {1}{x}\right )}d x}}{\int -\frac {{\mathrm e}^{\int \frac {-\ln \left (\frac {x^{2}+1}{x}\right ) x -\tanh \left (\frac {1}{x}\right )}{x \tanh \left (\frac {1}{x}\right )}d x} x \ln \left (\frac {x^{2}+1}{x}\right )}{\tanh \left (\frac {1}{x}\right )}d x +c_{1}}\]