2.984   ODE No. 984

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

$$y^{\prime }(x)=\frac{e^{-2x}(x-1)y(x)(x^{2}y(x{)}^2+e^{x}xy(x)+e^{2x})}{x}$$ ✓ Mathematica : cpu = 3.0444 (sec), leaf count = 428

$$\text{Solve}[\frac{\sqrt[3]{2}(\frac{3e^{-2x}x(x-1)y(x)+e^{-x}(x-1)}{\sqrt[3]{2}\sqrt[3]{e^{-3x}(x-1{)}^3}}+2^{2/3})(2^{2/3}-\frac{2^{2/3}(3e^{-2x}x(x-1)y(x)+e^{-x}(x-1))}{\sqrt[3]{e^{-3x}(x-1{)}^3}})((1-\frac{3e^{-2x}x(x-1)y(x)+e^{-x}(x-1)}{\sqrt[3]{e^{-3x}(x-1{)}^3}})\log (2^{2/3}-\frac{2^{2/3}(3e^{-2x}x(x-1)y(x)+e^{-x}(x-1))}{\sqrt[3]{e^{-3x}(x-1{)}^3}})+(\frac{3e^{-2x}x(x-1)y(x)+e^{-x}(x-1)}{\sqrt[3]{e^{-3x}(x-1{)}^3}}-1)\log \left(2(\frac{3e^{-2x}x(x-1)y(x)+e^{-x}(x-1)}{\sqrt[3]{2}\sqrt[3]{e^{-3x}(x-1{)}^3}}+2^{2/3})\right)-3)}{9(-\frac{e^{3x}{(3e^{-2x}x(x-1)y(x)+e^{-x}(x-1))}^3}{(x-1{)}^3}+\frac{3(3e^{-2x}x(x-1)y(x)+e^{-x}(x-1))}{\sqrt[3]{e^{-3x}(x-1{)}^3}}-2)}=c_1+\frac{2^{2/3}{e}^{-x}(x-1)(x-\log (x))}{9\sqrt[3]{e^{-3x}(x-1{)}^3}},y(x)]$$

✓ Maple : cpu = 0.281 (sec), leaf count = 40

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