\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {y \left ( x \right ) +\ln \left ( \left ( 1+x \right ) \left ( x-1 \right ) \right ) {x}^{3}+7\,\ln \left ( \left ( 1+x \right ) \left ( x-1 \right ) \right ) x \left ( y \left ( x \right ) \right ) ^{2}}{x}}=0} \]
Mathematica: cpu = 0.039005 (sec), leaf count = 87 \[ \left \{\left \{y(x)\to \frac {x \tan \left (\frac {1}{2} \left (2 \sqrt {7} c_1-\sqrt {7} x^2+\sqrt {7} x^2 \log (x-1)+\sqrt {7} x^2 \log (x+1)-\sqrt {7} \log (1-x)-\sqrt {7} \log (x+1)\right )\right )}{\sqrt {7}}\right \}\right \} \]
Maple: cpu = 0.047 (sec), leaf count = 48 \[ \left \{ y \left ( x \right ) ={\frac {x\sqrt {7}}{7}\tan \left ( {\frac { \left ( {x}^{2}\ln \left ( \left ( 1+x \right ) \left ( x-1 \right ) \right ) -{x}^{2}-\ln \left ( \left ( 1+x \right ) \left ( x-1 \right ) \right ) +2\,{\it \_C1}+1 \right ) \sqrt {7}}{2}} \right ) } \right \} \]