3.791   ODE No. 791

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=\frac{2x^2\cosh \left({(x-1)}^{-1}\right)-2x\cosh \left({(x-1)}^{-1}\right)-1+{\left(y\left(x\right)\right)}^2-2x^{2}y\left(x\right)+x^4-x+x{\left(y\left(x\right)\right)}^2-2x^{3}y\left(x\right)+x^5}{(x-1)\cosh \left({(x-1)}^{-1}\right)}=0}}$$

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

Mathematica: cpu = 1670.398114 (sec), leaf count = 87 $$\left\{\{y(x)\to \frac{\exp ({\int }_1^x\frac{2(K[5]+1)\text{sech}\left(\frac{1}{K[5]-1}\right)}{K[5]-1}dK[5])}{c_1-\frac{1}{2}\exp \left(\text{Integrate}[\frac{2(K[5]+1)\text{sech}\left(\frac{1}{K[5]-1}\right)}{K[5]-1},\{K[5],1,x\},\text{Assumptions}\to \text{True}]\right)}+\frac{x^3+x^2}{x+1}+1\}\right\}$$

Maple: cpu = 12.699 (sec), leaf count = 634 $$\{y\left(x\right)=1(x^2{\left({\mathrm{e}}^{\frac{\mathit{\_}\mathit{C}\mathit{1}}{{\left({\mathrm{e}}^{{(x-1)}^{-1}}\right)}^2+1}{\mathrm{e}}^{2{(x-1)}^{-1}}}\right)}^4{\left({\mathrm{e}}^{\frac{\mathit{\_}\mathit{C}\mathit{1}}{{\left({\mathrm{e}}^{{(x-1)}^{-1}}\right)}^2+1}}\right)}^4{\left({\mathrm{e}}^{\frac{1}{{\left({\mathrm{e}}^{{(x-1)}^{-1}}\right)}^2+1}\int {(\frac{{\mathrm{e}}^{{(x-1)}^{-1}}x}{1+x}+\frac{x}{{\mathrm{e}}^{{(x-1)}^{-1}}(1+x)}-\frac{{\mathrm{e}}^{{(x-1)}^{-1}}}{1+x}-\frac{1}{{\mathrm{e}}^{{(x-1)}^{-1}}(1+x)})}^{-1}\mathrm{d}x{\mathrm{e}}^{2{(x-1)}^{-1}}}\right)}^{-4}{\left({\mathrm{e}}^{\frac{1}{{\left({\mathrm{e}}^{{(x-1)}^{-1}}\right)}^2+1}\int {(\frac{{\mathrm{e}}^{{(x-1)}^{-1}}x}{1+x}+\frac{x}{{\mathrm{e}}^{{(x-1)}^{-1}}(1+x)}-\frac{{\mathrm{e}}^{{(x-1)}^{-1}}}{1+x}-\frac{1}{{\mathrm{e}}^{{(x-1)}^{-1}}(1+x)})}^{-1}\mathrm{d}x}\right)}^{-4}-x^2+1{\left({\mathrm{e}}^{\frac{\mathit{\_}\mathit{C}\mathit{1}}{{\left({\mathrm{e}}^{{(x-1)}^{-1}}\right)}^2+1}{\mathrm{e}}^{2{(x-1)}^{-1}}}\right)}^4{\left({\mathrm{e}}^{\frac{\mathit{\_}\mathit{C}\mathit{1}}{{\left({\mathrm{e}}^{{(x-1)}^{-1}}\right)}^2+1}}\right)}^4{\left({\mathrm{e}}^{\frac{1}{{\left({\mathrm{e}}^{{(x-1)}^{-1}}\right)}^2+1}\int {(\frac{{\mathrm{e}}^{{(x-1)}^{-1}}x}{1+x}+\frac{x}{{\mathrm{e}}^{{(x-1)}^{-1}}(1+x)}-\frac{{\mathrm{e}}^{{(x-1)}^{-1}}}{1+x}-\frac{1}{{\mathrm{e}}^{{(x-1)}^{-1}}(1+x)})}^{-1}\mathrm{d}x{\mathrm{e}}^{2{(x-1)}^{-1}}}\right)}^{-4}{\left({\mathrm{e}}^{\frac{1}{{\left({\mathrm{e}}^{{(x-1)}^{-1}}\right)}^2+1}\int {(\frac{{\mathrm{e}}^{{(x-1)}^{-1}}x}{1+x}+\frac{x}{{\mathrm{e}}^{{(x-1)}^{-1}}(1+x)}-\frac{{\mathrm{e}}^{{(x-1)}^{-1}}}{1+x}-\frac{1}{{\mathrm{e}}^{{(x-1)}^{-1}}(1+x)})}^{-1}\mathrm{d}x}\right)}^{-4}+1){(-1+1{\left({\mathrm{e}}^{\frac{\mathit{\_}\mathit{C}\mathit{1}}{{\left({\mathrm{e}}^{{(x-1)}^{-1}}\right)}^2+1}{\mathrm{e}}^{2{(x-1)}^{-1}}}\right)}^4{\left({\mathrm{e}}^{\frac{\mathit{\_}\mathit{C}\mathit{1}}{{\left({\mathrm{e}}^{{(x-1)}^{-1}}\right)}^2+1}}\right)}^4{\left({\mathrm{e}}^{\frac{1}{{\left({\mathrm{e}}^{{(x-1)}^{-1}}\right)}^2+1}\int {(\frac{{\mathrm{e}}^{{(x-1)}^{-1}}x}{1+x}+\frac{x}{{\mathrm{e}}^{{(x-1)}^{-1}}(1+x)}-\frac{{\mathrm{e}}^{{(x-1)}^{-1}}}{1+x}-\frac{1}{{\mathrm{e}}^{{(x-1)}^{-1}}(1+x)})}^{-1}\mathrm{d}x{\mathrm{e}}^{2{(x-1)}^{-1}}}\right)}^{-4}{\left({\mathrm{e}}^{\frac{1}{{\left({\mathrm{e}}^{{(x-1)}^{-1}}\right)}^2+1}\int {(\frac{{\mathrm{e}}^{{(x-1)}^{-1}}x}{1+x}+\frac{x}{{\mathrm{e}}^{{(x-1)}^{-1}}(1+x)}-\frac{{\mathrm{e}}^{{(x-1)}^{-1}}}{1+x}-\frac{1}{{\mathrm{e}}^{{(x-1)}^{-1}}(1+x)})}^{-1}\mathrm{d}x}\right)}^{-4})}^{-1}\}$$