3.255   ODE No. 255

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

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

Mathematica: cpu = 5.161155 (sec), leaf count = 31 $$\left\{\{y(x)\to -\frac{3W\left(2e^{\frac{9c_1}{2^{2/3}}-1}{x}^{2/3}\right)}{x}\}\right\}$$

Maple: cpu = 0.156 (sec), leaf count = 74 $$\{y\left(x\right)=-3\frac{\mathit{l}\mathit{a}\mathit{m}\mathit{b}\mathit{e}\mathit{r}\mathit{t}\mathit{W}\left(2/3\sqrt[3]{-1/8x^2}\mathit{\_}\mathit{C}\mathit{1}\right)}{x},y\left(x\right)=-3\frac{\mathit{l}\mathit{a}\mathit{m}\mathit{b}\mathit{e}\mathit{r}\mathit{t}\mathit{W}\left(1/3\sqrt[3]{-1/8x^2}\mathit{\_}\mathit{C}\mathit{1}(i\sqrt{3}-1)\right)}{x},y\left(x\right)=-3\frac{\mathit{l}\mathit{a}\mathit{m}\mathit{b}\mathit{e}\mathit{r}\mathit{t}\mathit{W}(-1/3\sqrt[3]{-1/8x^2}\mathit{\_}\mathit{C}\mathit{1}(i\sqrt{3}+1))}{x}\}$$