\[ y'(x)=\frac {-x^3+3 x^2 y(x)+x^2-3 x y(x)^2+y(x)^3}{(x-1) (x+1)} \] ✓ Mathematica : cpu = 0.254323 (sec), leaf count = 238
\[\text {Solve}\left [\frac {1}{3} \log \left (\frac {\frac {3 y(x)}{x^2-1}-\frac {3 x}{x^2-1}}{3 \sqrt [3]{\frac {1}{(x-1)^3 (x+1)^3}}}+1\right )-\frac {1}{6} \log \left (\frac {\left (\frac {3 y(x)}{x^2-1}-\frac {3 x}{x^2-1}\right )^2}{9 \left (\frac {1}{(x-1)^3 (x+1)^3}\right )^{2/3}}-\frac {\frac {3 y(x)}{x^2-1}-\frac {3 x}{x^2-1}}{3 \sqrt [3]{\frac {1}{(x-1)^3 (x+1)^3}}}+1\right )+\frac {\tan ^{-1}\left (\frac {\frac {2 \left (\frac {3 y(x)}{x^2-1}-\frac {3 x}{x^2-1}\right )}{3 \sqrt [3]{\frac {1}{(x-1)^3 (x+1)^3}}}-1}{\sqrt {3}}\right )}{\sqrt {3}}=c_1+\frac {1}{2} \left (\frac {1}{\left (x^2-1\right )^3}\right )^{2/3} \left (x^2-1\right )^2 (\log (1-x)-\log (x+1)),y(x)\right ]\]
✓ Maple : cpu = 0.278 (sec), leaf count = 469
\[ \left \{ y \left ( x \right ) ={\frac {\sqrt {3}}{6} \left ( \sqrt {3}\sqrt [3]{{\frac {1}{ \left ( 1+x \right ) ^{3} \left ( x-1 \right ) ^{3}}}}{x}^{2}+3\,\sqrt [3]{{\frac {1}{ \left ( 1+x \right ) ^{3} \left ( x-1 \right ) ^{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 ) {x}^{2}-\sqrt {3}\sqrt [3]{{\frac {1}{ \left ( 1+x \right ) ^{3} \left ( x-1 \right ) ^{3}}}}+2\,\sqrt {3}x-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]{{\frac {1}{ \left ( 1+x \right ) ^{3} \left ( x-1 \right ) ^{3}}}} \right ) } \right \} \]