3.28   ODE No. 28

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

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

Mathematica: cpu = 0.047006 (sec), leaf count = 96 $$\left\{\{y(x)\to \frac{c_1{e}^{\frac{x^4}{4}}{x}^3+\frac{1}{2}\sqrt{\pi }{e}^{\frac{x^4}{4}}{x}^3\text{erf}\left(\frac{x^2}{2}\right)+x}{x(c_1{e}^{\frac{x^4}{4}}+\frac{1}{2}\sqrt{\pi }{e}^{\frac{x^4}{4}}\text{erf}\left(\frac{x^2}{2}\right))}\}\right\}$$

Maple: cpu = 0.078 (sec), leaf count = 67 $$\{y\left(x\right)=2\frac{{\mathrm{e}}^{-1/4x^4}\mathit{\_}\mathit{C}\mathit{1}}{\sqrt{\pi }(\mathit{E}\mathit{r}\mathit{f}\left(1/2x^2\right)\mathit{\_}\mathit{C}\mathit{1}+1)}+\frac{1}{\sqrt{\pi }}(\mathit{E}\mathit{r}\mathit{f}\left(\frac{x^2}{2}\right)\sqrt{\pi }\mathit{\_}\mathit{C}\mathit{1}{x}^2+x^2\sqrt{\pi }){(\mathit{E}\mathit{r}\mathit{f}\left(\frac{x^2}{2}\right)\mathit{\_}\mathit{C}\mathit{1}+1)}^{-1}\}$$

Sage: cpu = 0.096 (sec), leaf count = 0 $$[[y\left(x\right)=\frac{((\sqrt{\pi }c\text{erf}\left(\frac{1}{2}{x}^2\right)+\sqrt{\pi })x^2{e}^{\left(\frac{1}{4}{x}^4\right)}+2c)e^{(-\frac{1}{4}{x}^4)}}{\sqrt{\pi }c\text{erf}\left(\frac{1}{2}{x}^2\right)+\sqrt{\pi }}],\mathtt{\text{riccati}}]$$