\[ y'(x)=\frac {-e^{x+1} x^3+e^{x+1} x y(x)^2+x y(x)-y(x)}{(x-1) x} \] ✓ Mathematica : cpu = 0.348341 (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 = 0.071 (sec), leaf count = 25
\[y \relax (x ) = -\tanh \left ({\mathrm e}^{1+x}-{\mathrm e}^{2} \Ei \left (1, 1-x \right )+c_{1}\right ) x\]