\[ y'(x)=\frac {e^{\frac {x+1}{x-1}} x^3+e^{\frac {x+1}{x-1}} x y(x)^2+y(x)}{x} \] ✓ Mathematica : cpu = 0.380523 (sec), leaf count = 82
DSolve[Derivative[1][y][x] == (E^((1 + x)/(-1 + x))*x^3 + y[x] + E^((1 + x)/(-1 + x))*x*y[x]^2)/x,y[x],x]
\[\left \{\left \{y(x)\to x \tan \left (\frac {1}{2} \left (-8 e \text {Ei}\left (\frac {2}{x-1}\right )+e^{\frac {x}{x-1}+\frac {1}{x-1}} x^2+2 e^{\frac {x}{x-1}+\frac {1}{x-1}} x-3 e^{\frac {x}{x-1}+\frac {1}{x-1}}+2 c_1\right )\right )\right \}\right \}\] ✓ Maple : cpu = 0.101 (sec), leaf count = 42
dsolve(diff(y(x),x) = (y(x)+exp((1+x)/(x-1))*x^3+exp((1+x)/(x-1))*x*y(x)^2)/x,y(x))
\[y \left (x \right ) = \tan \left (\frac {\left (x^{2}+2 x -3\right ) {\mathrm e}^{\frac {1+x}{x -1}}}{2}+4 \,{\mathrm e} \Ei \left (1, -\frac {2}{x -1}\right )+c_{1}\right ) x\]