\[ y'(x)=\frac {e^{x+1} x^3+7 e^{x+1} x y(x)^2+y(x) \log (x-1)}{x \log (x-1)} \] ✗ Mathematica : cpu = 299.998 (sec), leaf count = 0 , timed out
$Aborted
✓ Maple : cpu = 0.073 (sec), leaf count = 32
\[ \left \{ y \left ( x \right ) ={\frac {x\sqrt {7}}{7}\tan \left ( \left ( {\rm e}\int \!{\frac {x{{\rm e}^{x}}}{\ln \left ( x-1 \right ) }}\,{\rm d}x+{\it \_C1} \right ) \sqrt {7} \right ) } \right \} \]