\[ y'(x)=\frac {y(x) \left (x^2 y(x) \log \left (\frac {(x-1) (x+1)}{x}\right )-x \log \left (\frac {(x-1) (x+1)}{x}\right )-\log (x)\right )}{x \log (x)} \] ✓ Mathematica : cpu = 0.307829 (sec), leaf count = 129
\[\left \{\left \{y(x)\to \frac {\exp \left (\int _1^x\frac {-\log (K[1])-K[1] \log \left (\frac {(K[1]-1) (K[1]+1)}{K[1]}\right )}{K[1] \log (K[1])}dK[1]\right )}{-\int _1^x\frac {\exp \left (\int _1^{K[2]}\frac {-\log (K[1])-K[1] \log \left (\frac {(K[1]-1) (K[1]+1)}{K[1]}\right )}{K[1] \log (K[1])}dK[1]\right ) K[2] \log \left (\frac {(K[2]-1) (K[2]+1)}{K[2]}\right )}{\log (K[2])}dK[2]+c_1}\right \}\right \}\] ✓ Maple : cpu = 0.327 (sec), leaf count = 89
\[ \left \{ y \left ( x \right ) ={{{\rm e}^{\int \!{\frac {1}{x\ln \left ( x \right ) } \left ( -x\ln \left ( {\frac { \left ( 1+x \right ) \left ( x-1 \right ) }{x}} \right ) -\ln \left ( x \right ) \right ) }\,{\rm d}x}} \left ( \int \!-{\frac {x}{\ln \left ( x \right ) }{{\rm e}^{\int \!{\frac {1}{x\ln \left ( x \right ) } \left ( -x\ln \left ( {\frac { \left ( 1+x \right ) \left ( x-1 \right ) }{x}} \right ) -\ln \left ( x \right ) \right ) }\,{\rm d}x}}\ln \left ( {\frac { \left ( 1+x \right ) \left ( x-1 \right ) }{x}} \right ) }\,{\rm d}x+{\it \_C1} \right ) ^{-1}} \right \} \]