\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {y \left ( x \right ) }{x} \left ( -1-x{{\rm e}^{{\frac {1+x}{x-1}}}}+{x}^{2}{{\rm e}^{{\frac {1+x}{x-1}}}}y \left ( x \right ) -{x}^{2}{{\rm e}^{{\frac {1+x}{x-1}}}}+{x}^{3}{{\rm e}^{{\frac {1+x}{x-1}}}}y \left ( x \right ) \right ) }=0} \]
Mathematica: cpu = 0.300538 (sec), leaf count = 70 \[ \left \{\left \{y(x)\to \frac {e^{6 e \text {Ei}\left (\frac {2}{x-1}\right )}}{x \left (c_1 e^{\frac {1}{2} e^{\frac {x}{x-1}+\frac {1}{x-1}} \left (x^2+4 x-5\right )}+e^{6 e \text {Ei}\left (\frac {2}{x-1}\right )}\right )}\right \}\right \} \]
Maple: cpu = 0.234 (sec), leaf count = 147 \[ \left \{ y \left ( x \right ) ={\frac {1}{x}{{\rm e}^{{\frac {5}{2}{ {\rm e}^{{\frac {1+x}{x-1}}}}}}}{{\rm e}^{-{\frac {{x}^{2}}{2}{{\rm e} ^{{\frac {1+x}{x-1}}}}}}} \left ( {{\rm e}^{{\rm e}{\it Ei} \left ( 1,-2 \, \left ( x-1 \right ) ^{-1} \right ) }} \right ) ^{-6} \left ( {{\rm e}^{ x{{\rm e}^{{\frac {1+x}{x-1}}}}}} \right ) ^{-2} \left ( \int \!-{(1+x){ {\rm e}^{{\frac {1+x}{x-1}}}}{{\rm e}^{{\frac {5}{2}{{\rm e}^{{\frac { 1+x}{x-1}}}}}}}{{\rm e}^{-{\frac {{x}^{2}}{2}{{\rm e}^{{\frac {1+x}{x- 1}}}}}}} \left ( {{\rm e}^{{\rm e}{\it Ei} \left ( 1,-2\, \left ( x-1 \right ) ^{-1} \right ) }} \right ) ^{-6} \left ( {{\rm e}^{x{{\rm e}^{{ \frac {1+x}{x-1}}}}}} \right ) ^{-2}}\,{\rm d}x+{\it \_C1} \right ) ^{-1 }} \right \} \]