3.797   ODE No. 797

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

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

Mathematica: cpu = 2.027757 (sec), leaf count = 349 $$\left\{\{y(x)\to \frac{\exp (\frac{(3e^2-1)\text{Chi}\left(\frac{2}{x-1}\right)}{e}+\frac{(1+3e^2)\text{Shi}\left(\frac{2}{x-1}\right)}{e}-\frac{1}{4}e{x}^2\sinh \left(\frac{2}{x-1}\right)+\frac{x^2\sinh \left(\frac{2}{x-1}\right)}{4e}-\frac{1}{4}e{x}^2\cosh \left(\frac{2}{x-1}\right)-\frac{x^2\cosh \left(\frac{2}{x-1}\right)}{4e}-ex\sinh \left(\frac{2}{x-1}\right)+\frac{5}{4}e\sinh \left(\frac{2}{x-1}\right)-\frac{\sinh \left(\frac{2}{x-1}\right)}{4e}-ex\cosh \left(\frac{2}{x-1}\right)+\frac{5}{4}e\cosh \left(\frac{2}{x-1}\right)+\frac{\cosh \left(\frac{2}{x-1}\right)}{4e}+\frac{(x-1)((-x+e^2(x+5)-1)\sinh \left(\frac{2}{x-1}\right)+(x+e^2(x+5)+1)\cosh \left(\frac{2}{x-1}\right))}{4e})}{x(c_1\exp \left(\frac{(x-1)((-x+e^2(x+5)-1)\sinh \left(\frac{2}{x-1}\right)+(x+e^2(x+5)+1)\cosh \left(\frac{2}{x-1}\right))}{4e}\right)+\exp (\frac{(3e^2-1)\text{Chi}\left(\frac{2}{x-1}\right)}{e}+\frac{(1+3e^2)\text{Shi}\left(\frac{2}{x-1}\right)}{e}))}\}\right\}$$

Maple: cpu = 0.141 (sec), leaf count = 281 $$\{y\left(x\right)=\frac{1}{x}{\mathrm{e}}^{-\frac{\mathrm{e}{x}^2}{4}{\mathrm{e}}^{2{(x-1)}^{-1}}}{\mathrm{e}}^{\frac{5\mathrm{e}}{4}{\mathrm{e}}^{2{(x-1)}^{-1}}}{\mathrm{e}}^{-\frac{{\mathrm{e}}^{-1}{x}^2}{4}{\mathrm{e}}^{-2{(x-1)}^{-1}}}{\mathrm{e}}^{\frac{{\mathrm{e}}^{-1}}{4}{\mathrm{e}}^{-2{(x-1)}^{-1}}}{\mathrm{e}}^{{\mathrm{e}}^{-1}\mathit{E}\mathit{i}(1,2{(x-1)}^{-1})}{\left({\mathrm{e}}^{\mathrm{e}{\mathrm{e}}^{2{(x-1)}^{-1}}x}\right)}^{-1}{\left({\mathrm{e}}^{\mathrm{e}\mathit{E}\mathit{i}(1,-2{(x-1)}^{-1})}\right)}^{-3}{(\int -1{\mathrm{e}}^{-\frac{\mathrm{e}{x}^2}{4}{\mathrm{e}}^{2{(x-1)}^{-1}}}{\mathrm{e}}^{\frac{5\mathrm{e}}{4}{\mathrm{e}}^{2{(x-1)}^{-1}}}{\mathrm{e}}^{-\frac{{\mathrm{e}}^{-1}{x}^2}{4}{\mathrm{e}}^{-2{(x-1)}^{-1}}}{\mathrm{e}}^{\frac{{\mathrm{e}}^{-1}}{4}{\mathrm{e}}^{-2{(x-1)}^{-1}}}{\mathrm{e}}^{{\mathrm{e}}^{-1}\mathit{E}\mathit{i}(1,2{(x-1)}^{-1})}(x\cosh \left({(x-1)}^{-1}\right)\cosh \left(\frac{x}{x-1}\right)+x\sinh \left({(x-1)}^{-1}\right)\sinh \left(\frac{x}{x-1}\right)+\cosh \left({(x-1)}^{-1}\right)\cosh \left(\frac{x}{x-1}\right)+\sinh \left({(x-1)}^{-1}\right)\sinh \left(\frac{x}{x-1}\right)){\left({\mathrm{e}}^{\mathrm{e}{\mathrm{e}}^{2{(x-1)}^{-1}}x}\right)}^{-1}{\left({\mathrm{e}}^{\mathrm{e}\mathit{E}\mathit{i}(1,-2{(x-1)}^{-1})}\right)}^{-3}\mathrm{d}x+\mathit{\_}\mathit{C}\mathit{1})}^{-1}\}$$