3.301   ODE No. 301

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

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

Mathematica: cpu = 0.039005 (sec), leaf count = 64 $$\{\{y(x)\to -\frac{\sqrt{x}\sqrt{W\left(\frac{6e^{3c_1}}{x^3}\right)}}{\sqrt{6}}\},\{y(x)\to \frac{\sqrt{x}\sqrt{W\left(\frac{6e^{3c_1}}{x^3}\right)}}{\sqrt{6}}\}\}$$

Maple: cpu = 0.156 (sec), leaf count = 25 $$\{y\left(x\right)=\frac{1}{x}{\mathrm{e}}^{-\frac{1}{2}\mathit{l}\mathit{a}\mathit{m}\mathit{b}\mathit{e}\mathit{r}\mathit{t}\mathit{W}\left(6\frac{{\mathrm{e}}^{3\mathit{\_}\mathit{C}\mathit{1}}}{x^3}\right)+\frac{3\mathit{\_}\mathit{C}\mathit{1}}{2}}\}$$