\[ y'(x)=\frac {x^3 \log ((x-1) (x+1))+y(x)+7 x y(x)^2 \log ((x-1) (x+1))}{x} \] ✓ Mathematica : cpu = 0.152912 (sec), leaf count = 87
DSolve[Derivative[1][y][x] == (x^3*Log[(-1 + x)*(1 + x)] + y[x] + 7*x*Log[(-1 + x)*(1 + x)]*y[x]^2)/x,y[x],x]
\[\left \{\left \{y(x)\to \frac {x \tan \left (\frac {1}{2} \left (-\sqrt {7} x^2+\sqrt {7} x^2 \log (x-1)+\sqrt {7} x^2 \log (x+1)-\sqrt {7} \log (1-x)-\sqrt {7} \log (x+1)+2 \sqrt {7} c_1\right )\right )}{\sqrt {7}}\right \}\right \}\] ✓ Maple : cpu = 0.093 (sec), leaf count = 48
dsolve(diff(y(x),x) = (y(x)+ln((x-1)*(1+x))*x^3+7*ln((x-1)*(1+x))*x*y(x)^2)/x,y(x))
\[y \left (x \right ) = \frac {\tan \left (\frac {\left (x^{2} \ln \left (\left (x -1\right ) \left (1+x \right )\right )-x^{2}-\ln \left (\left (x -1\right ) \left (1+x \right )\right )+2 c_{1}+1\right ) \sqrt {7}}{2}\right ) x \sqrt {7}}{7}\]