\[ y'(x)=\frac {e^{x+1} x^3+7 e^{x+1} x y(x)^2+y(x) \log (x-1)}{x \log (x-1)} \] ✓ Mathematica : cpu = 1.11497 (sec), leaf count = 51
\[\left \{\left \{y(x)\to \frac {x \tan \left (\sqrt {7} \int _1^x\frac {e^{K[1]+1} K[1]}{\log (K[1]-1)}dK[1]+\sqrt {7} c_1\right )}{\sqrt {7}}\right \}\right \}\] ✓ Maple : cpu = 0.077 (sec), leaf count = 32
\[\left \{y \left (x \right ) = \frac {\sqrt {7}\, x \tan \left (\left (c_{1}+{\mathrm e} \left (\int \frac {x \,{\mathrm e}^{x}}{\ln \left (x -1\right )}d x \right )\right ) \sqrt {7}\right )}{7}\right \}\]