3.846   ODE No. 846

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

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

Mathematica: cpu = 1.356672 (sec), leaf count = 362 $$\text{Solve}[{\int }_1^{y(x)}(\frac{x\mathrm{\_}\text{F1}\left(x(\frac{1}{K[2]}+1)\right)-1}{xK[2]\mathrm{\_}\text{F1}\left(x(\frac{1}{K[2]}+1)\right)+x\mathrm{\_}\text{F1}\left(x(\frac{1}{K[2]}+1)\right)-K[2]}-{\int }_1^x(\frac{-\frac{K[1]{\mathrm{\_}\text{F1}}^{\prime }(K[1](\frac{1}{K[2]}+1))}{K[2]}-\frac{K[1]{\mathrm{\_}\text{F1}}^{\prime }(K[1](\frac{1}{K[2]}+1))}{K[2{]}^2}+\mathrm{\_}\text{F1}(K[1](\frac{1}{K[2]}+1))}{K[1](K[2]\mathrm{\_}\text{F1}(K[1](\frac{1}{K[2]}+1))+\mathrm{\_}\text{F1}(K[1](\frac{1}{K[2]}+1)))-K[2]}-\frac{(K[2]\mathrm{\_}\text{F1}(K[1](\frac{1}{K[2]}+1))+\mathrm{\_}\text{F1}(K[1](\frac{1}{K[2]}+1)))(K[1](-\frac{K[1]{\mathrm{\_}\text{F1}}^{\prime }(K[1](\frac{1}{K[2]}+1))}{K[2]}-\frac{K[1]{\mathrm{\_}\text{F1}}^{\prime }(K[1](\frac{1}{K[2]}+1))}{K[2{]}^2}+\mathrm{\_}\text{F1}(K[1](\frac{1}{K[2]}+1)))-1)}{(K[1](K[2]\mathrm{\_}\text{F1}(K[1](\frac{1}{K[2]}+1))+\mathrm{\_}\text{F1}(K[1](\frac{1}{K[2]}+1)))-K[2]){}^2})dK[1])dK[2]+{\int }_1^x(\frac{y(x)\mathrm{\_}\text{F1}((\frac{1}{y(x)}+1)K[1])+\mathrm{\_}\text{F1}((\frac{1}{y(x)}+1)K[1])}{K[1](y(x)\mathrm{\_}\text{F1}((\frac{1}{y(x)}+1)K[1])+\mathrm{\_}\text{F1}((\frac{1}{y(x)}+1)K[1]))-y(x)}-\frac{1}{K[1]})dK[1]=c_1,y(x)]$$

Maple: cpu = 0.141 (sec), leaf count = 40 $$\{y\left(x\right)={\mathrm{e}}^{\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-\mathit{\_}\mathit{Z}-{\int }^{\frac{x{\mathrm{e}}^{\mathit{\_}\mathit{Z}}}{{\mathrm{e}}^{\mathit{\_}\mathit{Z}}-1}}\frac{1}{(\mathit{\_}\mathit{F}\mathit{1}\left(\mathit{\_}\mathit{a}\right)\mathit{\_}\mathit{a}-1)\mathit{\_}\mathit{a}}d\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1})}-1\}$$