3.683   ODE No. 683

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=\frac{y\left(x\right)(-1+\ln \left(x(1+x)\right)y\left(x\right)x^4-\ln \left(x(1+x)\right)x^3)}{x}=0}}$$

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

Mathematica: cpu = 0.361046 (sec), leaf count = 84 $$\left\{\{y(x)\to \frac{e^{\frac{2x^3}{9}+\frac{x}{3}}}{c_1{e}^{\frac{x^2}{6}}x\sqrt[3]{x+1}(x(x+1){)}^{\frac{x^3}{3}}+e^{\frac{x^2}{6}+\frac{1}{18}(4x^2-3x+6)x}x}\}\right\}$$

Maple: cpu = 0.109 (sec), leaf count = 166 $$\{y\left(x\right)=\frac{1}{x}{\left(x(1+x)\right)}^{-\frac{x^3}{3}}{\mathrm{e}}^{\frac{2x^3}{9}}{\mathrm{e}}^{-\frac{x^2}{6}}{\mathrm{e}}^{\frac{x}{3}}{(x^{-\frac{x^3}{3}}{(1+x)}^{-\frac{x^3}{3}}{\mathrm{e}}^{\frac{x(3i{x}^2{\left(\mathit{c}\mathit{s}\mathit{g}\mathit{n}\left(ix(1+x)\right)\right)}^3\pi -3i{x}^2{\left(\mathit{c}\mathit{s}\mathit{g}\mathit{n}\left(ix(1+x)\right)\right)}^2\mathit{c}\mathit{s}\mathit{g}\mathit{n}\left(ix\right)\pi -3i{x}^2{\left(\mathit{c}\mathit{s}\mathit{g}\mathit{n}\left(ix(1+x)\right)\right)}^2\mathit{c}\mathit{s}\mathit{g}\mathit{n}\left(i(1+x)\right)\pi +3i{x}^2\mathit{c}\mathit{s}\mathit{g}\mathit{n}\left(ix(1+x)\right)\mathit{c}\mathit{s}\mathit{g}\mathit{n}\left(ix\right)\mathit{c}\mathit{s}\mathit{g}\mathit{n}\left(i(1+x)\right)\pi +4x^2-3x+6)}{18}}+\mathit{\_}\mathit{C}\mathit{1}\sqrt[3]{1+x})}^{-1}\}$$