\[ y'(x)=\frac {-e^{x+1} x^3+e^{x+1} x y(x)^2+x y(x)-y(x)}{(x-1) x} \] ✓ Mathematica : cpu = 0.0683742 (sec), leaf count = 60
\[\left \{\left \{y(x)\to -\frac {x \left (e^{2 c_1+2 e^2 \text {Ei}(x-1)+2 e^{x+1}}-1\right )}{e^{2 c_1+2 e^2 \text {Ei}(x-1)+2 e^{x+1}}+1}\right \}\right \}\] ✓ Maple : cpu = 0.054 (sec), leaf count = 25
\[ \left \{ y \left ( x \right ) =-\tanh \left ( {{\rm e}^{1+x}}-{{\rm e}^{2}}{\it Ei} \left ( 1,1-x \right ) +{\it \_C1} \right ) x \right \} \]