\[ y'(x)=\frac {-x^3+3 x^2 y(x)+x^2-3 x y(x)^2+y(x)^3}{(x-1) (x+1)} \] ✓ Mathematica : cpu = 0.520806 (sec), leaf count = 176
\[\text {Solve}\left [\frac {1}{6} \left (-\log \left (\left (\frac {1}{\left (x^2-1\right )^3}\right )^{2/3} \left (x^2-1\right )^2 (x-y(x))+\frac {(x-y(x))^2}{\left (\frac {1}{\left (x^2-1\right )^3}\right )^{2/3} \left (x^2-1\right )^2}+1\right )+2 \log \left (\frac {y(x)-x}{\sqrt [3]{\frac {1}{\left (x^2-1\right )^3}} \left (x^2-1\right )}+1\right )+2 \sqrt {3} \tan ^{-1}\left (\frac {-2 \left (\frac {1}{\left (x^2-1\right )^3}\right )^{2/3} \left (x^2-1\right )^2 (x-y(x))-1}{\sqrt {3}}\right )\right )=c_1+\frac {1}{2} \left (\frac {1}{\left (x^2-1\right )^3}\right )^{2/3} \left (x^2-1\right )^2 (\log (1-x)-\log (x+1)),y(x)\right ]\]
✓ Maple : cpu = 0.869 (sec), leaf count = 188
\[ \left \{ y \left ( x \right ) ={\frac {\sqrt {3}}{2} \left ( {\frac {{x}^{2}-1}{3} \left ( 3\,\tan \left ( {\it RootOf} \left ( 9\, \left ( {\frac {1}{ \left ( 1+x \right ) ^{3} \left ( x-1 \right ) ^{3}}} \right ) ^{2/3}\ln \left ( {\frac {x-1}{1+x}} \right ) {x}^{4}-18\, \left ( {\frac {1}{ \left ( 1+x \right ) ^{3} \left ( x-1 \right ) ^{3}}} \right ) ^{2/3}\ln \left ( {\frac {x-1}{1+x}} \right ) {x}^{2}+9\, \left ( {\frac {1}{ \left ( 1+x \right ) ^{3} \left ( x-1 \right ) ^{3}}} \right ) ^{2/3}\ln \left ( {\frac {x-1}{1+x}} \right ) -6\,{\it \_Z}\,\sqrt {3}-3\,\ln \left ( 4/3\, \left ( \left ( \tan \left ( {\it \_Z} \right ) \right ) ^{2}+1 \right ) ^{-1} \right ) -2\,\ln \left ( 3/8\,{\frac { \left ( \sqrt {3}+\tan \left ( {\it \_Z} \right ) \right ) ^{3}\sqrt {3}}{ \left ( 1+x \right ) ^{3} \left ( x-1 \right ) ^{3}}} \right ) +2\,\ln \left ( {\frac {1}{ \left ( 1+x \right ) ^{3} \left ( x-1 \right ) ^{3}}} \right ) +18\,{\it \_C1} \right ) \right ) +\sqrt {3} \right ) \sqrt [3]{{\frac {1}{ \left ( 1+x \right ) ^{3} \left ( x-1 \right ) ^{3}}}}}+{\frac {2\,\sqrt {3}x}{3}} \right ) } \right \} \]