\[ y'(x)=\frac {y(x) \left (e^{\frac {x+1}{x-1}} x^3 y(x)+e^{\frac {x+1}{x-1}} x^2 y(x)-e^{\frac {x+1}{x-1}} x^2-e^{\frac {x+1}{x-1}} x-1\right )}{x} \] ✓ Mathematica : cpu = 0.831036 (sec), leaf count = 64
DSolve[Derivative[1][y][x] == (y[x]*(-1 - E^((1 + x)/(-1 + x))*x - E^((1 + x)/(-1 + x))*x^2 + E^((1 + x)/(-1 + x))*x^2*y[x] + E^((1 + x)/(-1 + x))*x^3*y[x]))/x,y[x],x]
\[\left \{\left \{y(x)\to \frac {e^{6 e \operatorname {ExpIntegralEi}\left (\frac {2}{x-1}\right )}}{x \left (e^{6 e \operatorname {ExpIntegralEi}\left (\frac {2}{x-1}\right )}+c_1 e^{\frac {1}{2} e^{\frac {2}{x-1}+1} (x-1) (x+5)}\right )}\right \}\right \}\] ✓ Maple : cpu = 0.321 (sec), leaf count = 147
dsolve(diff(y(x),x) = y(x)*(-1-x*exp((1+x)/(x-1))+x^2*exp((1+x)/(x-1))*y(x)-x^2*exp((1+x)/(x-1))+x^3*exp((1+x)/(x-1))*y(x))/x,y(x))
\[y \left (x \right ) = \frac {{\mathrm e}^{\frac {5 \,{\mathrm e}^{\frac {1+x}{x -1}}}{2}} {\mathrm e}^{-\frac {x^{2} {\mathrm e}^{\frac {1+x}{x -1}}}{2}} {\mathrm e}^{-2 x \,{\mathrm e}^{\frac {1+x}{x -1}}} {\mathrm e}^{-6 \,{\mathrm e} \,\operatorname {expIntegral}_{1}\left (-\frac {2}{x -1}\right )}}{x \left (c_{1}+\int -\left (1+x \right ) {\mathrm e}^{\frac {1+x}{x -1}} {\mathrm e}^{\frac {5 \,{\mathrm e}^{\frac {1+x}{x -1}}}{2}} {\mathrm e}^{-\frac {x^{2} {\mathrm e}^{\frac {1+x}{x -1}}}{2}} {\mathrm e}^{-2 x \,{\mathrm e}^{\frac {1+x}{x -1}}} {\mathrm e}^{-6 \,{\mathrm e} \,\operatorname {expIntegral}_{1}\left (-\frac {2}{x -1}\right )}d x \right )}\]