\[ y'(x)=\frac {-x^3+3 x^2 y(x)+x^2-3 x y(x)^2+y(x)^3}{(x-1) (x+1)} \] ✗ Mathematica : cpu = 300.002 (sec), leaf count = 0 , timed out
$Aborted
✓ Maple : cpu = 0.409 (sec), leaf count = 233
\[ \left \{ y \left ( x \right ) ={\frac {\sqrt {3}}{2} \left ( {\frac {{x}^{2}-1}{3} \left ( 3\,\tan \left ( {\it RootOf} \left ( -18\,\ln \left ( 1+x \right ) \left ( {\frac {1}{ \left ( 1+x \right ) ^{3} \left ( x-1 \right ) ^{3}}} \right ) ^{2/3}{x}^{4}+18\,\ln \left ( x-1 \right ) \left ( {\frac {1}{ \left ( 1+x \right ) ^{3} \left ( x-1 \right ) ^{3}}} \right ) ^{2/3}{x}^{4}+36\,\ln \left ( 1+x \right ) \left ( {\frac {1}{ \left ( 1+x \right ) ^{3} \left ( x-1 \right ) ^{3}}} \right ) ^{2/3}{x}^{2}-36\,\ln \left ( x-1 \right ) \left ( {\frac {1}{ \left ( 1+x \right ) ^{3} \left ( x-1 \right ) ^{3}}} \right ) ^{2/3}{x}^{2}-18\, \left ( {\frac {1}{ \left ( 1+x \right ) ^{3} \left ( x-1 \right ) ^{3}}} \right ) ^{2/3}\ln \left ( 1+x \right ) +18\, \left ( {\frac {1}{ \left ( 1+x \right ) ^{3} \left ( x-1 \right ) ^{3}}} \right ) ^{2/3}\ln \left ( x-1 \right ) -12\,{\it \_Z}\,\sqrt {3}-6\,\ln \left ( 4/3\, \left ( \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}+1 \right ) ^{-1} \right ) -4\,\ln \left ( 3/8\,{\frac { \left ( \sqrt {3}+\tan \left ( {\it \_Z} \right ) \right ) ^{3}\sqrt {3}}{ \left ( 1+x \right ) ^{3} \left ( x-1 \right ) ^{3}}} \right ) +4\,\ln \left ( {\frac {1}{ \left ( 1+x \right ) ^{3} \left ( x-1 \right ) ^{3}}} \right ) +36\,{\it \_C1} \right ) \right ) +\sqrt {3} \right ) \sqrt [3]{{\frac {1}{ \left ( 1+x \right ) ^{3} \left ( x-1 \right ) ^{3}}}}}+{\frac {2\,\sqrt {3}x}{3}} \right ) } \right \} \]