2.844   ODE No. 844

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

$$y^{\prime }(x)=\frac{y(x)(y(x)+1)(y(x)+x)}{x(xy(x)+y(x)+x)}$$ ✓ Mathematica : cpu = 10.4817 (sec), leaf count = 386

$$\text{Solve}[\frac{2^{2/3}(1-\frac{{\left(\frac{x^6}{(x+1{)}^3}\right)}^{2/3}(x+1{)}^2((x-2)y(x)+x)}{x^4((x+1)y(x)+x)})(\frac{{\left(\frac{x^6}{(x+1{)}^3}\right)}^{2/3}(x+1{)}^2((x-2)y(x)+x)}{x^4((x+1)y(x)+x)}+2)((1-\frac{{\left(\frac{x^6}{(x+1{)}^3}\right)}^{2/3}(x+1{)}^2((x-2)y(x)+x)}{x^4((x+1)y(x)+x)})\log \left(2^{2/3}(1-\frac{{\left(\frac{x^6}{(x+1{)}^3}\right)}^{2/3}(x+1{)}^2((x-2)y(x)+x)}{x^4((x+1)y(x)+x)})\right)+(\frac{{\left(\frac{x^6}{(x+1{)}^3}\right)}^{2/3}(x+1{)}^2((x-2)y(x)+x)}{x^4((x+1)y(x)+x)}-1)\log \left(2^{2/3}(\frac{{\left(\frac{x^6}{(x+1{)}^3}\right)}^{2/3}(x+1{)}^2((x-2)y(x)+x)}{x^4((x+1)y(x)+x)}+2)\right)-3)}{9(\frac{3{\left(\frac{x^6}{(x+1{)}^3}\right)}^{2/3}(x+1{)}^2((x-2)y(x)+x)}{x^4((x+1)y(x)+x)}-\frac{((x-2)y(x)+x{)}^3}{((x+1)y(x)+x{)}^3}-2)}=\frac{2^{2/3}{\left(\frac{x^6}{(x+1{)}^3}\right)}^{2/3}(x+1{)}^2}{9x^3}+c_1,y(x)]$$ ✓ Maple : cpu = 1.039 (sec), leaf count = 97

$$\{y\left(x\right)=-x{\mathrm{e}}^{\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-\ln (\frac{{\mathrm{e}}^{\mathit{\_}\mathit{Z}}}{2}+\frac{9}{2}){\mathrm{e}}^{\mathit{\_}\mathit{Z}}+3{\mathrm{e}}^{\mathit{\_}\mathit{Z}}\mathit{\_}\mathit{C}\mathit{1}+\mathit{\_}\mathit{Z}{\mathrm{e}}^{\mathit{\_}\mathit{Z}}+x{\mathrm{e}}^{\mathit{\_}\mathit{Z}}+9)}{({\mathrm{e}}^{\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-\ln (\frac{{\mathrm{e}}^{\mathit{\_}\mathit{Z}}}{2}+\frac{9}{2}){\mathrm{e}}^{\mathit{\_}\mathit{Z}}+3{\mathrm{e}}^{\mathit{\_}\mathit{Z}}\mathit{\_}\mathit{C}\mathit{1}+\mathit{\_}\mathit{Z}{\mathrm{e}}^{\mathit{\_}\mathit{Z}}+x{\mathrm{e}}^{\mathit{\_}\mathit{Z}}+9)}x+{\mathrm{e}}^{\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-\ln (\frac{{\mathrm{e}}^{\mathit{\_}\mathit{Z}}}{2}+\frac{9}{2}){\mathrm{e}}^{\mathit{\_}\mathit{Z}}+3{\mathrm{e}}^{\mathit{\_}\mathit{Z}}\mathit{\_}\mathit{C}\mathit{1}+\mathit{\_}\mathit{Z}{\mathrm{e}}^{\mathit{\_}\mathit{Z}}+x{\mathrm{e}}^{\mathit{\_}\mathit{Z}}+9)}+9)}^{-1}\}$$