\[ y'(x)=\frac {-e^{x+1} x^3+e^{x+1} x y(x)^2+x y(x)-y(x)}{(x-1) x} \] ✓ Mathematica : cpu = 0.328563 (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 = 0.184 (sec), leaf count = 25
\[ \left \{ y \left ( x \right ) =-\tanh \left ( {{\rm e}^{1+x}}-{{\rm e}^{2}}{\it Ei} \left ( 1,1-x \right ) +{\it \_C1} \right ) x \right \} \]