3.728   ODE No. 728

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

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

Mathematica: cpu = 0.434555 (sec), leaf count = 72 $$\{\{y(x)\to -\frac{\sqrt{x}\sqrt{W\left(\frac{6e^{2c_1+x^2}}{x}\right)}}{\sqrt{6}}\},\{y(x)\to \frac{\sqrt{x}\sqrt{W\left(\frac{6e^{2c_1+x^2}}{x}\right)}}{\sqrt{6}}\}\}$$

Maple: cpu = 0.234 (sec), leaf count = 50 $$\{{({\left(y\left(x\right)\right)}^{-2}+6x^{-1})}^{-1}=\frac{x}{54}({\mathrm{e}}^{\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}({\mathrm{e}}^{\mathit{\_}\mathit{Z}}{x}^2-{\mathrm{e}}^{\mathit{\_}\mathit{Z}}\ln \left(\frac{({\mathrm{e}}^{\mathit{\_}\mathit{Z}}+9)x}{2}\right)+3{\mathrm{e}}^{\mathit{\_}\mathit{Z}}\mathit{\_}\mathit{C}\mathit{1}+\mathit{\_}\mathit{Z}{\mathrm{e}}^{\mathit{\_}\mathit{Z}}+9)}+9)\}$$