\[ y'(x)=\frac {e^{x+1} x^3+7 e^{x+1} x y(x)^2+y(x) \log (x-1)}{x \log (x-1)} \] ✓ Mathematica : cpu = 0.951418 (sec), leaf count = 51
DSolve[Derivative[1][y][x] == (E^(1 + x)*x^3 + Log[-1 + x]*y[x] + 7*E^(1 + x)*x*y[x]^2)/(x*Log[-1 + x]),y[x],x]
\[\left \{\left \{y(x)\to \frac {x \tan \left (\sqrt {7} \int _1^x\frac {e^{K[1]+1} K[1]}{\log (K[1]-1)}dK[1]+\sqrt {7} c_1\right )}{\sqrt {7}}\right \}\right \}\] ✓ Maple : cpu = 0.075 (sec), leaf count = 32
dsolve(diff(y(x),x) = (y(x)*ln(x-1)+exp(1+x)*x^3+7*exp(1+x)*x*y(x)^2)/ln(x-1)/x,y(x))
\[y \left (x \right ) = \frac {\tan \left (\left ({\mathrm e} \left (\int \frac {x \,{\mathrm e}^{x}}{\ln \left (x -1\right )}d x \right )+c_{1}\right ) \sqrt {7}\right ) x \sqrt {7}}{7}\]