3.984   ODE No. 984

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

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

Mathematica: cpu = 3.039386 (sec), leaf count = 426 $$\text{Solve}[-\frac{\sqrt[3]{2}(\frac{3e^{-2x}x(x-1)y(x)+e^{-x}(x-1)}{\sqrt[3]{2}\sqrt[3]{e^{-3x}(x-1{)}^3}}+2^{2/3})(2^{2/3}-\frac{2^{2/3}(3e^{-2x}x(x-1)y(x)+e^{-x}(x-1))}{\sqrt[3]{e^{-3x}(x-1{)}^3}})((1-\frac{3e^{-2x}x(x-1)y(x)+e^{-x}(x-1)}{\sqrt[3]{e^{-3x}(x-1{)}^3}})\log (\frac{3e^{-2x}x(x-1)y(x)+e^{-x}(x-1)}{\sqrt[3]{2}\sqrt[3]{e^{-3x}(x-1{)}^3}}+2^{2/3})+(\frac{3e^{-2x}x(x-1)y(x)+e^{-x}(x-1)}{\sqrt[3]{e^{-3x}(x-1{)}^3}}-1)\log (2^{2/3}-\frac{2^{2/3}(3e^{-2x}x(x-1)y(x)+e^{-x}(x-1))}{\sqrt[3]{e^{-3x}(x-1{)}^3}})+3)}{9(-\frac{e^{3x}{(3e^{-2x}x(x-1)y(x)+e^{-x}(x-1))}^3}{(x-1{)}^3}+\frac{3(3e^{-2x}x(x-1)y(x)+e^{-x}(x-1))}{\sqrt[3]{e^{-3x}(x-1{)}^3}}-2)}=c_1+\frac{2^{2/3}{e}^{-x}(x-1)(x-\log (x))}{9\sqrt[3]{e^{-3x}(x-1{)}^3}},y(x)]$$

Maple: cpu = 0.203 (sec), leaf count = 40 $$\{y\left(x\right)=\frac{1}{9x}{\mathrm{e}}^{\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-{\mathrm{e}}^{\mathit{\_}\mathit{Z}}\ln \left(\frac{x({\mathrm{e}}^{\mathit{\_}\mathit{Z}}+9)}{2}\right)+3\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{\mathit{\_}\mathit{Z}}+\mathit{\_}\mathit{Z}{\mathrm{e}}^{\mathit{\_}\mathit{Z}}+x{\mathrm{e}}^{\mathit{\_}\mathit{Z}}+9)+x}\}$$