2.799   ODE No. 799

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

$$y^{\prime }(x)=\frac{y(x)(e^{\frac{x+1}{x-1}}{x}^{3}y(x)+e^{\frac{x+1}{x-1}}{x}^{2}y(x)-e^{\frac{x+1}{x-1}}{x}^2-e^{\frac{x+1}{x-1}}x-1)}{x}$$ ✓ Mathematica : cpu = 1.1045 (sec), leaf count = 126

$$\left\{\{y(x)\to \frac{\exp (6e\text{Ei}\left(\frac{2}{x-1}\right)+\frac{1}{2}{e}^{\frac{x}{x-1}+\frac{1}{x-1}}(x^2+4x-5)-e^{\frac{2}{x-1}}(\frac{1}{2}e(x-1{)}^2+3e(x-1)))}{x(e^{6e\text{Ei}\left(\frac{2}{x-1}\right)}+c_1{e}^{\frac{1}{2}{e}^{\frac{x}{x-1}+\frac{1}{x-1}}(x^2+4x-5)})}\}\right\}$$ ✓ Maple : cpu = 0.429 (sec), leaf count = 147

$$\{y\left(x\right)=\frac{1}{x}{\mathrm{e}}^{\frac{5}{2}{\mathrm{e}}^{\frac{1+x}{x-1}}}{\mathrm{e}}^{-\frac{x^2}{2}{\mathrm{e}}^{\frac{1+x}{x-1}}}{\left({\mathrm{e}}^{\mathrm{e}\mathit{E}\mathit{i}(1,-2{(x-1)}^{-1})}\right)}^{-6}{\left({\mathrm{e}}^{x{\mathrm{e}}^{\frac{1+x}{x-1}}}\right)}^{-2}{(\int -(1+x){\mathrm{e}}^{\frac{1+x}{x-1}}{\mathrm{e}}^{\frac{5}{2}{\mathrm{e}}^{\frac{1+x}{x-1}}}{\mathrm{e}}^{-\frac{x^2}{2}{\mathrm{e}}^{\frac{1+x}{x-1}}}{\left({\mathrm{e}}^{\mathrm{e}\mathit{E}\mathit{i}(1,-2{(x-1)}^{-1})}\right)}^{-6}{\left({\mathrm{e}}^{x{\mathrm{e}}^{\frac{1+x}{x-1}}}\right)}^{-2}\mathrm{d}x+\mathit{\_}\mathit{C}\mathit{1})}^{-1}\}$$