\[ y'(x)=\frac {e^{\frac {x+1}{x-1}} x^3+e^{\frac {x+1}{x-1}} x y(x)^2+y(x)}{x} \] ✓ Mathematica : cpu = 0.351181 (sec), leaf count = 82
\[\left \{\left \{y(x)\to x \tan \left (\frac {1}{2} \left (-8 e \text {Ei}\left (\frac {2}{x-1}\right )+e^{\frac {x}{x-1}+\frac {1}{x-1}} x^2+2 e^{\frac {x}{x-1}+\frac {1}{x-1}} x-3 e^{\frac {x}{x-1}+\frac {1}{x-1}}+2 c_1\right )\right )\right \}\right \}\] ✓ Maple : cpu = 0.22 (sec), leaf count = 42
\[ \left \{ y \left ( x \right ) =\tan \left ( {\frac {{x}^{2}+2\,x-3}{2}{{\rm e}^{{\frac {1+x}{x-1}}}}}+4\,{\rm e}{\it Ei} \left ( 1,-2\, \left ( x-1 \right ) ^{-1} \right ) +{\it \_C1} \right ) x \right \} \]