\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac {1}{x} \left ( y \left ( x \right ) +{{\rm e}^{{\frac {1+x}{x-1}}}}{x}^{3}+{{\rm e}^{{\frac {1+x}{x-1}}}}x \left ( y \left ( x \right ) \right ) ^{2} \right ) }=0} \]
Mathematica: cpu = 0.116515 (sec), leaf count = 78 \[ \left \{\left \{y(x)\to x \tan \left (\frac {1}{2} \left (2 c_1-8 e \text {Ei}\left (\frac {2}{x-1}\right )+e^{\frac {x}{x-1}+\frac {1}{x-1}} x^2+2 e^{\frac {x}{x-1}+\frac {1}{x-1}} x-3 e^{\frac {2}{x-1}+1}\right )\right )\right \}\right \} \]
Maple: cpu = 0.062 (sec), leaf count = 61 \[ \left \{ y \left ( x \right ) =\tan \left ( {\frac {{x}^{2}}{2}{{\rm e}^{ {\frac {1+x}{x-1}}}}}+x{{\rm e}^{{\frac {1+x}{x-1}}}}+4\,{\rm e}{\it Ei} \left ( 1,-2\, \left ( x-1 \right ) ^{-1} \right ) -{\frac {3}{2}{ {\rm e}^{{\frac {1+x}{x-1}}}}}+{\it \_C1} \right ) x \right \} \]