3.799   ODE No. 799

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=\frac{y\left(x\right)}{x}(-1-x{\mathrm{e}}^{\frac{1+x}{x-1}}+x^2{\mathrm{e}}^{\frac{1+x}{x-1}}y\left(x\right)-x^2{\mathrm{e}}^{\frac{1+x}{x-1}}+x^3{\mathrm{e}}^{\frac{1+x}{x-1}}y\left(x\right))=0}}$$

1. Problem in Latex
2. Mathematica input
3. Maple input

Mathematica: cpu = 0.300538 (sec), leaf count = 70 $$\left\{\{y(x)\to \frac{e^{6e\text{Ei}\left(\frac{2}{x-1}\right)}}{x(c_1{e}^{\frac{1}{2}{e}^{\frac{x}{x-1}+\frac{1}{x-1}}(x^2+4x-5)}+e^{6e\text{Ei}\left(\frac{2}{x-1}\right)})}\}\right\}$$

Maple: cpu = 0.234 (sec), leaf count = 147 $$\{y\left(x\right)=\frac{1}{x}{\mathrm{e}}^{\frac{5}{2}{\mathrm{e}}^{\frac{1+x}{x-1}}}{\mathrm{e}}^{-\frac{x^2}{2}{\mathrm{e}}^{\frac{1+x}{x-1}}}{\left({\mathrm{e}}^{\mathrm{e}\mathit{E}\mathit{i}(1,-2{(x-1)}^{-1})}\right)}^{-6}{\left({\mathrm{e}}^{x{\mathrm{e}}^{\frac{1+x}{x-1}}}\right)}^{-2}{(\int -(1+x){\mathrm{e}}^{\frac{1+x}{x-1}}{\mathrm{e}}^{\frac{5}{2}{\mathrm{e}}^{\frac{1+x}{x-1}}}{\mathrm{e}}^{-\frac{x^2}{2}{\mathrm{e}}^{\frac{1+x}{x-1}}}{\left({\mathrm{e}}^{\mathrm{e}\mathit{E}\mathit{i}(1,-2{(x-1)}^{-1})}\right)}^{-6}{\left({\mathrm{e}}^{x{\mathrm{e}}^{\frac{1+x}{x-1}}}\right)}^{-2}\mathrm{d}x+\mathit{\_}\mathit{C}\mathit{1})}^{-1}\}$$