3.781   ODE No. 781

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=\frac{(x^4+x^3+x+3{\left(y\left(x\right)\right)}^2)y\left(x\right)}{(6{\left(y\left(x\right)\right)}^2+x)x}=0}}$$

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

Mathematica: cpu = 0.495563 (sec), leaf count = 82 $$\{\{y(x)\to -\frac{\sqrt{x}\sqrt{W\left(6x{e}^{2c_1+\frac{2x^3}{3}+x^2}\right)}}{\sqrt{6}}\},\{y(x)\to \frac{\sqrt{x}\sqrt{W\left(6x{e}^{2c_1+\frac{2x^3}{3}+x^2}\right)}}{\sqrt{6}}\}\}$$

Maple: cpu = 0.249 (sec), leaf count = 61 $$\{{({\left(y\left(x\right)\right)}^{-2}+6x^{-1})}^{-1}=\frac{x}{54}({\mathrm{e}}^{\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(2x^3{\mathrm{e}}^{\mathit{\_}\mathit{Z}}+3{\mathrm{e}}^{\mathit{\_}\mathit{Z}}{x}^2-3{\mathrm{e}}^{\mathit{\_}\mathit{Z}}\ln \left(1/2\frac{{\mathrm{e}}^{\mathit{\_}\mathit{Z}}+9}{x}\right)+9{\mathrm{e}}^{\mathit{\_}\mathit{Z}}\mathit{\_}\mathit{C}\mathit{1}+3\mathit{\_}\mathit{Z}{\mathrm{e}}^{\mathit{\_}\mathit{Z}}+27)}+9)\}$$