3.320   ODE No. 320

$$\boxed{{\displaystyle (x^2{\left(y\left(x\right)\right)}^3+xy\left(x\right))\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)-1=0}}$$

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

Mathematica: cpu = 0.057007 (sec), leaf count = 76 $$\{\{y(x)\to -\frac{\sqrt{2xW\left(c_1{e}^{\frac{1}{2x}-1}\right)+2x-1}}{\sqrt{x}}\},\{y(x)\to \frac{\sqrt{2xW\left(c_1{e}^{\frac{1}{2x}-1}\right)+2x-1}}{\sqrt{x}}\}\}$$

Maple: cpu = 0.078 (sec), leaf count = 70 $$\{y\left(x\right)=\frac{1}{x}\sqrt{x(2\mathit{l}\mathit{a}\mathit{m}\mathit{b}\mathit{e}\mathit{r}\mathit{t}\mathit{W}\left(1/2\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{-1/2\frac{2x-1}{x}}\right)x+2x-1)},y\left(x\right)=-\frac{1}{x}\sqrt{x(2\mathit{l}\mathit{a}\mathit{m}\mathit{b}\mathit{e}\mathit{r}\mathit{t}\mathit{W}\left(1/2\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{-1/2\frac{2x-1}{x}}\right)x+2x-1)}\}$$