\[ y'(x)=\frac {-e^{x+1} x^3+e^{x+1} x y(x)^2+x y(x)-y(x)}{(x-1) x} \] ✓ Mathematica : cpu = 0.348341 (sec), leaf count = 60
DSolve[Derivative[1][y][x] == (-(E^(1 + x)*x^3) - y[x] + x*y[x] + E^(1 + x)*x*y[x]^2)/((-1 + x)*x),y[x],x]
\[\left \{\left \{y(x)\to -\frac {x \left (-1+e^{2 e^2 \text {Ei}(x-1)+2 e^{x+1}+2 c_1}\right )}{1+e^{2 e^2 \text {Ei}(x-1)+2 e^{x+1}+2 c_1}}\right \}\right \}\] ✓ Maple : cpu = 0.071 (sec), leaf count = 25
dsolve(diff(y(x),x) = (x*y(x)-y(x)-exp(1+x)*x^3+exp(1+x)*x*y(x)^2)/(x-1)/x,y(x))
\[y \left (x \right ) = -\tanh \left ({\mathrm e}^{1+x}-{\mathrm e}^{2} \Ei \left (1, 1-x \right )+c_{1}\right ) x\]