#### 2.799   ODE No. 799

$y'(x)=\frac {y(x) \left (e^{\frac {x+1}{x-1}} x^3 y(x)+e^{\frac {x+1}{x-1}} x^2 y(x)-e^{\frac {x+1}{x-1}} x^2-e^{\frac {x+1}{x-1}} x-1\right )}{x}$ Mathematica : cpu = 1.06124 (sec), leaf count = 126

$\left \{\left \{y(x)\to \frac {\exp \left (6 e \text {Ei}\left (\frac {2}{x-1}\right )+\frac {1}{2} e^{\frac {x}{x-1}+\frac {1}{x-1}} \left (x^2+4 x-5\right )-e^{\frac {2}{x-1}} \left (\frac {1}{2} e (x-1)^2+3 e (x-1)\right )\right )}{x \left (c_1 e^{\frac {1}{2} e^{\frac {x}{x-1}+\frac {1}{x-1}} \left (x^2+4 x-5\right )}+e^{6 e \text {Ei}\left (\frac {2}{x-1}\right )}\right )}\right \}\right \}$ Maple : cpu = 0.236 (sec), leaf count = 147

$\left \{ y \left ( x \right ) ={\frac {1}{x}{{\rm e}^{{\frac {5}{2}{{\rm e}^{{\frac {1+x}{x-1}}}}}}}{{\rm e}^{-{\frac {{x}^{2}}{2}{{\rm e}^{{\frac {1+x}{x-1}}}}}}} \left ( {{\rm e}^{{\it Ei} \left ( 1,-2\, \left ( x-1 \right ) ^{-1} \right ) {\rm e}}} \right ) ^{-6} \left ( {{\rm e}^{x{{\rm e}^{{\frac {1+x}{x-1}}}}}} \right ) ^{-2} \left ( \int \!-{(1+x){{\rm e}^{{\frac {1+x}{x-1}}}}{{\rm e}^{{\frac {5}{2}{{\rm e}^{{\frac {1+x}{x-1}}}}}}}{{\rm e}^{-{\frac {{x}^{2}}{2}{{\rm e}^{{\frac {1+x}{x-1}}}}}}} \left ( {{\rm e}^{{\it Ei} \left ( 1,-2\, \left ( x-1 \right ) ^{-1} \right ) {\rm e}}} \right ) ^{-6} \left ( {{\rm e}^{x{{\rm e}^{{\frac {1+x}{x-1}}}}}} \right ) ^{-2}}\,{\rm d}x+{\it \_C1} \right ) ^{-1}} \right \}$