\[ y'(x)=\frac {y(x) \left (x y(x) \log \left (\frac {(x-1) (x+1)}{x}\right )-\log \left (\frac {(x-1) (x+1)}{x}\right )-1\right )}{x} \] ✓ Mathematica : cpu = 0.342893 (sec), leaf count = 138
\[\left \{\left \{y(x)\to \frac {\exp \left (-\text {Li}_2(1-x)+\text {Li}_2(-x)-\frac {1}{2} \log ^2(x)+\log (x+1) \log (x)-\log \left (x-\frac {1}{x}\right ) \log (x)\right )}{x \left (-\int _1^x\frac {\exp \left (-\frac {1}{2} \log ^2(K[1])+\log (K[1]+1) \log (K[1])-\log \left (K[1]-\frac {1}{K[1]}\right ) \log (K[1])-\text {Li}_2(1-K[1])+\text {Li}_2(-K[1])\right ) \log \left (\frac {(K[1]-1) (K[1]+1)}{K[1]}\right )}{K[1]}dK[1]+c_1\right )}\right \}\right \}\] ✓ Maple : cpu = 0.464 (sec), leaf count = 106
\[ \left \{ y \left ( x \right ) ={\frac {{{\rm e}^{{\it dilog} \left ( 1+x \right ) }}{x}^{\ln \left ( 1+x \right ) }}{x{{\rm e}^{{\it dilog} \left ( x \right ) }}}{{\rm e}^{-{\frac { \left ( \ln \left ( x \right ) \right ) ^{2}}{2}}}} \left ( {x}^{\ln \left ( {\frac { \left ( 1+x \right ) \left ( x-1 \right ) }{x}} \right ) } \right ) ^{-1} \left ( \int \!-{\frac {{{\rm e}^{{\it dilog} \left ( 1+x \right ) }}{x}^{\ln \left ( 1+x \right ) }}{x{{\rm e}^{{\it dilog} \left ( x \right ) }}}{{\rm e}^{-{\frac { \left ( \ln \left ( x \right ) \right ) ^{2}}{2}}}}\ln \left ( {\frac { \left ( 1+x \right ) \left ( x-1 \right ) }{x}} \right ) \left ( {x}^{\ln \left ( {\frac { \left ( 1+x \right ) \left ( x-1 \right ) }{x}} \right ) } \right ) ^{-1}}\,{\rm d}x+{\it \_C1} \right ) ^{-1}} \right \} \]