\[ y'(x)=\frac {x^3 \log ((x-1) (x+1))+y(x)+7 x y(x)^2 \log ((x-1) (x+1))}{x} \] ✓ Mathematica : cpu = 0.136537 (sec), leaf count = 87
\[\left \{\left \{y(x)\to \frac {x \tan \left (\frac {1}{2} \left (-\sqrt {7} x^2+\sqrt {7} x^2 \log (x-1)+\sqrt {7} x^2 \log (x+1)-\sqrt {7} \log (1-x)-\sqrt {7} \log (x+1)+2 \sqrt {7} c_1\right )\right )}{\sqrt {7}}\right \}\right \}\] ✓ Maple : cpu = 0.289 (sec), leaf count = 48
\[ \left \{ y \left ( x \right ) ={\frac {x\sqrt {7}}{7}\tan \left ( {\frac { \left ( {x}^{2}\ln \left ( \left ( 1+x \right ) \left ( x-1 \right ) \right ) -{x}^{2}-\ln \left ( \left ( 1+x \right ) \left ( x-1 \right ) \right ) +2\,{\it \_C1}+1 \right ) \sqrt {7}}{2}} \right ) } \right \} \]