\[ y'(x)=\frac {-e^{x+1} x^3+e^{x+1} x y(x)^2+x y(x)-y(x)}{(x-1) x} \] ✓ Mathematica : cpu = 0.39464 (sec), leaf count = 60
\[\left \{\left \{y(x)\to -\frac {x \left (-1+e^{2 e^2 \text {Ei}(x-1)+2 e^{x+1}+2 c_1}\right )}{1+e^{2 e^2 \text {Ei}(x-1)+2 e^{x+1}+2 c_1}}\right \}\right \}\] ✓ Maple : cpu = 0.069 (sec), leaf count = 25
\[\{y \left (x \right ) = -x \tanh \left (c_{1}-{\mathrm e}^{2} \Ei \left (1, -x +1\right )+{\mathrm e}^{x +1}\right )\}\]