3.844   ODE No. 844

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

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

Mathematica: cpu = 16.574105 (sec), leaf count = 386 $$\text{Solve}[-\frac{2^{2/3}(1-\frac{{\left(\frac{x^6}{(x+1{)}^3}\right)}^{2/3}(x+1{)}^2((x-2)y(x)+x)}{x^4((x+1)y(x)+x)})(\frac{{\left(\frac{x^6}{(x+1{)}^3}\right)}^{2/3}(x+1{)}^2((x-2)y(x)+x)}{x^4((x+1)y(x)+x)}+2)((1-\frac{{\left(\frac{x^6}{(x+1{)}^3}\right)}^{2/3}(x+1{)}^2((x-2)y(x)+x)}{x^4((x+1)y(x)+x)})\log \left(\frac{\frac{{\left(\frac{x^6}{(x+1{)}^3}\right)}^{2/3}(x+1{)}^2((x-2)y(x)+x)}{x^4((x+1)y(x)+x)}+2}{\sqrt[3]{2}}\right)+(\frac{{\left(\frac{x^6}{(x+1{)}^3}\right)}^{2/3}(x+1{)}^2((x-2)y(x)+x)}{x^4((x+1)y(x)+x)}-1)\log \left(2^{2/3}(1-\frac{{\left(\frac{x^6}{(x+1{)}^3}\right)}^{2/3}(x+1{)}^2((x-2)y(x)+x)}{x^4((x+1)y(x)+x)})\right)+3)}{9(\frac{3{\left(\frac{x^6}{(x+1{)}^3}\right)}^{2/3}(x+1{)}^2((x-2)y(x)+x)}{x^4((x+1)y(x)+x)}-\frac{((x-2)y(x)+x{)}^3}{((x+1)y(x)+x{)}^3}-2)}=c_1+\frac{2^{2/3}{\left(\frac{x^6}{(x+1{)}^3}\right)}^{2/3}(x+1{)}^2}{9x^3},y(x)]$$

Maple: cpu = 0.140 (sec), leaf count = 97 $$\{y\left(x\right)=-x{\mathrm{e}}^{\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-\ln (\frac{{\mathrm{e}}^{\mathit{\_}\mathit{Z}}}{2}+\frac{9}{2}){\mathrm{e}}^{\mathit{\_}\mathit{Z}}+3\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{\mathit{\_}\mathit{Z}}+\mathit{\_}\mathit{Z}{\mathrm{e}}^{\mathit{\_}\mathit{Z}}+x{\mathrm{e}}^{\mathit{\_}\mathit{Z}}+9)}{({\mathrm{e}}^{\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-\ln (\frac{{\mathrm{e}}^{\mathit{\_}\mathit{Z}}}{2}+\frac{9}{2}){\mathrm{e}}^{\mathit{\_}\mathit{Z}}+3\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{\mathit{\_}\mathit{Z}}+\mathit{\_}\mathit{Z}{\mathrm{e}}^{\mathit{\_}\mathit{Z}}+x{\mathrm{e}}^{\mathit{\_}\mathit{Z}}+9)}x+{\mathrm{e}}^{\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-\ln (\frac{{\mathrm{e}}^{\mathit{\_}\mathit{Z}}}{2}+\frac{9}{2}){\mathrm{e}}^{\mathit{\_}\mathit{Z}}+3\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{\mathit{\_}\mathit{Z}}+\mathit{\_}\mathit{Z}{\mathrm{e}}^{\mathit{\_}\mathit{Z}}+x{\mathrm{e}}^{\mathit{\_}\mathit{Z}}+9)}+9)}^{-1}\}$$