2.683   ODE No. 683

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

$$y^{\prime }(x)=\frac{y(x)(x^{4}y(x)\log (x(x+1))-x^3\log (x(x+1))-1)}{x}$$ ✓ Mathematica : cpu = 1.0741 (sec), leaf count = 84

$$\left\{\{y(x)\to \frac{e^{\frac{2x^3}{9}+\frac{x}{3}}}{e^{\frac{x^2}{6}+\frac{1}{18}(4x^2-3x+6)x}x+c_1{e}^{\frac{x^2}{6}}x\sqrt[3]{x+1}(x(x+1){)}^{\frac{x^3}{3}}}\}\right\}$$ ✓ Maple : cpu = 0.368 (sec), leaf count = 114

$$\{y\left(x\right)={\left({\left(x(1+x)\right)}^{\frac{x^3}{3}}\right)}^{-1}{(\sqrt[3]{1+x}{\mathrm{e}}^{-\frac{2x^3}{9}+\frac{x^2}{6}-\frac{x}{3}}\mathit{\_}\mathit{C}\mathit{1}x+x^{1-\frac{x^3}{3}}{(1+x)}^{-\frac{x^3}{3}}{\mathrm{e}}^{\frac{i}{6}{x}^3(\mathit{c}\mathit{s}\mathit{g}\mathit{n}(i+ix)-\mathit{c}\mathit{s}\mathit{g}\mathit{n}\left(ix(1+x)\right))(-\mathit{c}\mathit{s}\mathit{g}\mathit{n}\left(ix(1+x)\right)+\mathit{c}\mathit{s}\mathit{g}\mathit{n}\left(ix\right))\mathit{c}\mathit{s}\mathit{g}\mathit{n}\left(ix(1+x)\right)\pi })}^{-1}\}$$