3.793   ODE No. 793

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

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

Mathematica: cpu = 13.841758 (sec), leaf count = 397 $$\text{Solve}[\frac{\sqrt[3]{-2}(\frac{2^{2/3}((x-1)y(x)-2)}{\sqrt[3]{-\frac{1}{(x-1{)}^3}}(x-1)((x-1)y(x)+1)}+(-2{)}^{2/3})(\frac{-xy(x)+y(x)+2}{\sqrt[3]{2}\sqrt[3]{-\frac{1}{(x-1{)}^3}}(x-1)((x-1)y(x)+1)}+(-2{)}^{2/3})((\frac{\sqrt[3]{-1}(-xy(x)+y(x)+2)}{\sqrt[3]{-\frac{1}{(x-1{)}^3}}(x-1)((x-1)y(x)+1)}+1)\log (\frac{2^{2/3}((x-1)y(x)-2)}{\sqrt[3]{-\frac{1}{(x-1{)}^3}}(x-1)((x-1)y(x)+1)}+(-2{)}^{2/3})-(\frac{\sqrt[3]{-1}(-xy(x)+y(x)+2)}{\sqrt[3]{-\frac{1}{(x-1{)}^3}}(x-1)((x-1)y(x)+1)}+1)\log (\frac{-xy(x)+y(x)+2}{\sqrt[3]{2}\sqrt[3]{-\frac{1}{(x-1{)}^3}}(x-1)((x-1)y(x)+1)}+(-2{)}^{2/3})-3)}{9(\frac{((x-1)y(x)-2{)}^3}{((x-1)y(x)+1{)}^3}+\frac{3\sqrt[3]{-1}((x-1)y(x)-2)}{{(-\frac{1}{(x-1{)}^3})}^{4/3}(x-1{)}^4((x-1)y(x)+1)}+2)}=c_1+\frac{1}{9}{2}^{2/3}{(-\frac{1}{(x-1{)}^3})}^{2/3}(x-1{)}^2(\log (1-x)-\log (x)),y(x)]$$

Maple: cpu = 0.078 (sec), leaf count = 32 $$\{y\left(x\right)=-2\frac{1}{x}{\mathrm{e}}^{-\mathit{l}\mathit{a}\mathit{m}\mathit{b}\mathit{e}\mathit{r}\mathit{t}\mathit{W}(-2\frac{(x-1){\left({\mathrm{e}}^{\mathit{\_}\mathit{C}\mathit{1}}\right)}^3{\mathrm{e}}^{-1}}{x})+3\mathit{\_}\mathit{C}\mathit{1}-1}\}$$