\[ y'(x)=\frac {y(x) \left (x y(x) \log \left (\frac {(x-1) (x+1)}{x}\right )-\log \left (\frac {(x-1) (x+1)}{x}\right )-1\right )}{x} \] ✓ Mathematica : cpu = 0.348267 (sec), leaf count = 138
DSolve[Derivative[1][y][x] == (y[x]*(-1 - Log[((-1 + x)*(1 + x))/x] + x*Log[((-1 + x)*(1 + x))/x]*y[x]))/x,y[x],x]
\[\left \{\left \{y(x)\to \frac {\exp \left (-\text {Li}_2(1-x)+\text {Li}_2(-x)-\frac {1}{2} \log ^2(x)+\log (x+1) \log (x)-\log \left (x-\frac {1}{x}\right ) \log (x)\right )}{x \left (-\int _1^x\frac {\exp \left (-\frac {1}{2} \log ^2(K[1])+\log (K[1]+1) \log (K[1])-\log \left (K[1]-\frac {1}{K[1]}\right ) \log (K[1])-\text {Li}_2(1-K[1])+\text {Li}_2(-K[1])\right ) \log \left (\frac {(K[1]-1) (K[1]+1)}{K[1]}\right )}{K[1]}dK[1]+c_1\right )}\right \}\right \}\] ✓ Maple : cpu = 0.208 (sec), leaf count = 106
dsolve(diff(y(x),x) = y(x)*(-1-ln((x-1)*(1+x)/x)+ln((x-1)*(1+x)/x)*x*y(x))/x,y(x))
\[y \left (x \right ) = \frac {{\mathrm e}^{\dilog \left (1+x \right )} x^{\ln \left (1+x \right )} {\mathrm e}^{-\frac {\ln \left (x \right )^{2}}{2}} x^{-\ln \left (\frac {\left (x -1\right ) \left (1+x \right )}{x}\right )} {\mathrm e}^{-\dilog \left (x \right )}}{x \left (\int -\frac {x^{-\ln \left (\frac {\left (x -1\right ) \left (1+x \right )}{x}\right )} {\mathrm e}^{\dilog \left (1+x \right )} x^{\ln \left (1+x \right )} {\mathrm e}^{-\dilog \left (x \right )} {\mathrm e}^{-\frac {\ln \left (x \right )^{2}}{2}} \ln \left (\frac {\left (x -1\right ) \left (1+x \right )}{x}\right )}{x}d x +c_{1}\right )}\]