\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {y \left ( x \right ) \ln \left ( x-1 \right ) +{{\rm e}^{1+x}}{x}^{3}+7\,{{\rm e}^{1+x}}x \left ( y \left ( x \right ) \right ) ^{2}}{\ln \left ( x-1 \right ) x}}=0} \]
Mathematica: cpu = 121.909981 (sec), leaf count = 50 \[ \left \{\left \{y(x)\to \frac {x \tan \left (\sqrt {7} \int _1^x \frac {e^{K[1]+1} K[1]}{\log (K[1]-1)} \, dK[1]+\sqrt {7} c_1\right )}{\sqrt {7}}\right \}\right \} \]
Maple: cpu = 0.047 (sec), leaf count = 32 \[ \left \{ y \left ( x \right ) ={\frac {x\sqrt {7}}{7}\tan \left ( \left ( {\rm e}\int \!{\frac {x{{\rm e}^{x}}}{\ln \left ( x-1 \right ) }}\,{\rm d}x+{\it \_C1} \right ) \sqrt {7} \right ) } \right \} \]