3.18   ODE No. 18

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

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

Mathematica: cpu = 0.020503 (sec), leaf count = 50 $$\left\{\{y(x)\to \frac{e^{\frac{x^2}{2}-2x}}{c_1-\frac{\sqrt{\frac{\pi }{2}}\text{erfi}\left(\frac{x-2}{\sqrt{2}}\right)}{e^2}}-1\}\right\}$$

Maple: cpu = 0.062 (sec), leaf count = 47 $$\{y\left(x\right)=-1+\frac{1}{\mathit{\_}\mathit{C}\mathit{1}+\frac{i}{2}\sqrt{\pi }{\mathrm{e}}^{-2}\sqrt{2}\mathit{E}\mathit{r}\mathit{f}(\frac{i}{2}\sqrt{2}x-i\sqrt{2})}{\mathrm{e}}^{\frac{x^2}{2}-2x}\}$$

Sage: cpu = 0.076 (sec), leaf count = 0 $$[[y\left(x\right)=-\frac{\sqrt{\pi }c{e}^2+\sqrt{\pi }\text{erf}\left(\frac{1}{2}\sqrt{2}(ix-2i)\right)+i\sqrt{2}{e}^{\left(\frac{1}{2}{(x-2)}^2\right)}}{\sqrt{\pi }c{e}^2+\sqrt{\pi }\text{erf}\left(\frac{1}{2}\sqrt{2}(ix-2i)\right)}],\mathtt{\text{riccati}}]$$