\[ y'(x)=\frac {y(x) \left (x^2 y(x) \log \left (\frac {(x-1) (x+1)}{x}\right )-x \log \left (\frac {(x-1) (x+1)}{x}\right )-\log (x)\right )}{x \log (x)} \] ✓ Mathematica : cpu = 0.313138 (sec), leaf count = 129
DSolve[Derivative[1][y][x] == (y[x]*(-Log[x] - x*Log[((-1 + x)*(1 + x))/x] + x^2*Log[((-1 + x)*(1 + x))/x]*y[x]))/(x*Log[x]),y[x],x]
\[\left \{\left \{y(x)\to \frac {\exp \left (\int _1^x\frac {-\log (K[1])-K[1] \log \left (\frac {(K[1]-1) (K[1]+1)}{K[1]}\right )}{K[1] \log (K[1])}dK[1]\right )}{-\int _1^x\frac {\exp \left (\int _1^{K[2]}\frac {-\log (K[1])-K[1] \log \left (\frac {(K[1]-1) (K[1]+1)}{K[1]}\right )}{K[1] \log (K[1])}dK[1]\right ) K[2] \log \left (\frac {(K[2]-1) (K[2]+1)}{K[2]}\right )}{\log (K[2])}dK[2]+c_1}\right \}\right \}\] ✓ Maple : cpu = 0.202 (sec), leaf count = 89
dsolve(diff(y(x),x) = y(x)*(-ln(x)-x*ln((x-1)*(1+x)/x)+ln((x-1)*(1+x)/x)*x^2*y(x))/x/ln(x),y(x))
\[y \left (x \right ) = \frac {{\mathrm e}^{\int \frac {-x \ln \left (\frac {\left (x -1\right ) \left (1+x \right )}{x}\right )-\ln \left (x \right )}{x \ln \left (x \right )}d x}}{\int -\frac {{\mathrm e}^{\int \frac {-x \ln \left (\frac {\left (x -1\right ) \left (1+x \right )}{x}\right )-\ln \left (x \right )}{x \ln \left (x \right )}d x} x \ln \left (\frac {\left (x -1\right ) \left (1+x \right )}{x}\right )}{\ln \left (x \right )}d x +c_{1}}\]