\[ y'(x)=\frac {y(x) \left (x y(x) \log \left (\frac {(x-1) (x+1)}{x}\right )-\log \left (\frac {(x-1) (x+1)}{x}\right )-1\right )}{x} \] ✗ Mathematica : cpu = 299.998 (sec), leaf count = 0 , timed out
$Aborted
✓ Maple : cpu = 0.236 (sec), leaf count = 106
\[ \left \{ y \left ( x \right ) ={\frac {{{\rm e}^{{\it dilog} \left ( 1+x \right ) }}{x}^{\ln \left ( 1+x \right ) }}{x{{\rm e}^{{\it dilog} \left ( x \right ) }}}{{\rm e}^{-{\frac { \left ( \ln \left ( x \right ) \right ) ^{2}}{2}}}} \left ( \int \!-{\frac {{{\rm e}^{{\it dilog} \left ( 1+x \right ) }}{x}^{\ln \left ( 1+x \right ) }}{x{{\rm e}^{{\it dilog} \left ( x \right ) }}}{{\rm e}^{-{\frac { \left ( \ln \left ( x \right ) \right ) ^{2}}{2}}}}\ln \left ( {\frac { \left ( x-1 \right ) \left ( 1+x \right ) }{x}} \right ) \left ( {x}^{\ln \left ( {\frac { \left ( x-1 \right ) \left ( 1+x \right ) }{x}} \right ) } \right ) ^{-1}}\,{\rm d}x+{\it \_C1} \right ) ^{-1} \left ( {x}^{\ln \left ( {\frac { \left ( x-1 \right ) \left ( 1+x \right ) }{x}} \right ) } \right ) ^{-1}} \right \} \]