2.861   ODE No. 861

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

$$y^{\prime }(x)=-\frac{e^{-1/x}(-\mathrm{\_}\text{F1}(e^{\frac{1}{x}}y(x))-\frac{e^{\frac{1}{x}}y(x)}{x})}{x}$$ ✓ Mathematica : cpu = 1.86509 (sec), leaf count = 155

$$\text{Solve}[{\int }_1^{y(x)}-\frac{\mathrm{\_}\text{F1}(e^{\frac{1}{x}}K[2])({\int }_1^x(\frac{e^{\frac{1}{K[1]}}}{K[1{]}^2\mathrm{\_}\text{F1}(e^{\frac{1}{K[1]}}K[2])}-\frac{e^{\frac{2}{K[1]}}K[2]{\mathrm{\_}\text{F1}}^{\prime }(e^{\frac{1}{K[1]}}K[2])}{K[1{]}^2\left(\mathrm{\_}\text{F1}(e^{\frac{1}{K[1]}}K[2])\right){}^2})dK[1])+e^{\frac{1}{x}}}{\mathrm{\_}\text{F1}(e^{\frac{1}{x}}K[2])}dK[2]+{\int }_1^x(\frac{y(x)e^{\frac{1}{K[1]}}}{K[1{]}^2\mathrm{\_}\text{F1}(y(x)e^{\frac{1}{K[1]}})}+\frac{1}{K[1]})dK[1]=c_1,y(x)]$$

✓ Maple : cpu = 0.178 (sec), leaf count = 26

$$\{y\left(x\right)=\frac{\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-\ln \left(x\right)+{\int }^{\mathit{\_}\mathit{Z}}{\left(\mathit{\_}\mathit{F}\mathit{1}\left(\mathit{\_}\mathit{a}\right)\right)}^{-1}d\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1})}{{\mathrm{e}}^{x^{-1}}}\}$$