\[ y'(x)=\frac {y(x) \left (e^{\frac {x+1}{x-1}} x^3 y(x)+e^{\frac {x+1}{x-1}} x^2 y(x)-e^{\frac {x+1}{x-1}} x^2-e^{\frac {x+1}{x-1}} x-1\right )}{x} \] ✓ Mathematica : cpu = 1.088 (sec), leaf count = 126
\[\left \{\left \{y(x)\to \frac {\exp \left (6 e \text {Ei}\left (\frac {2}{x-1}\right )+\frac {1}{2} e^{\frac {x}{x-1}+\frac {1}{x-1}} \left (x^2+4 x-5\right )-e^{\frac {2}{x-1}} \left (\frac {1}{2} e (x-1)^2+3 e (x-1)\right )\right )}{x \left (e^{6 e \text {Ei}\left (\frac {2}{x-1}\right )}+c_1 e^{\frac {1}{2} e^{\frac {x}{x-1}+\frac {1}{x-1}} \left (x^2+4 x-5\right )}\right )}\right \}\right \}\] ✓ Maple : cpu = 0.271 (sec), leaf count = 147
\[y \relax (x ) = \frac {{\mathrm e}^{\frac {5 \,{\mathrm e}^{\frac {1+x}{x -1}}}{2}} {\mathrm e}^{-\frac {x^{2} {\mathrm e}^{\frac {1+x}{x -1}}}{2}} {\mathrm e}^{-6 \Ei \left (1, -\frac {2}{x -1}\right ) {\mathrm e}} {\mathrm e}^{-2 x \,{\mathrm e}^{\frac {1+x}{x -1}}}}{x \left (\int -\left (1+x \right ) {\mathrm e}^{\frac {1+x}{x -1}} {\mathrm e}^{\frac {5 \,{\mathrm e}^{\frac {1+x}{x -1}}}{2}} {\mathrm e}^{-\frac {x^{2} {\mathrm e}^{\frac {1+x}{x -1}}}{2}} {\mathrm e}^{-2 x \,{\mathrm e}^{\frac {1+x}{x -1}}} {\mathrm e}^{-6 \Ei \left (1, -\frac {2}{x -1}\right ) {\mathrm e}}d x +c_{1}\right )}\]