\[ y'(x)=\frac {x^3 \log ((x-1) (x+1))+y(x)+7 x y(x)^2 \log ((x-1) (x+1))}{x} \] ✓ Mathematica : cpu = 0.193616 (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 = 0.097 (sec), leaf count = 48
\[\left \{y \left (x \right ) = \frac {\sqrt {7}\, x \tan \left (\frac {\left (x^{2} \ln \left (\left (x -1\right ) \left (x +1\right )\right )-x^{2}+2 c_{1}-\ln \left (\left (x -1\right ) \left (x +1\right )\right )+1\right ) \sqrt {7}}{2}\right )}{7}\right \}\]