3.20   ODE No. 20

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

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

Mathematica: cpu = 0.789600 (sec), leaf count = 48 $$\left\{\{y(x)\to \frac{e^{\frac{x^3}{3}+x}}{c_1-{\int }_1^x{e}^{\frac{K[1{]}^3}{3}+K[1]}dK[1]}+x^2+1\}\right\}$$

Maple: cpu = 0.062 (sec), leaf count = 34 $$\{y\left(x\right)=x^2+1+1{\mathrm{e}}^{\frac{x^3}{3}+x}{(\mathit{\_}\mathit{C}\mathit{1}-\int {\mathrm{e}}^{\frac{x^3}{3}+x}\mathrm{d}x)}^{-1}\}$$

Sage: cpu = 0.244 (sec), leaf count = 0 $$[[y\left(x\right)=\frac{c{x}^2+(x^2+1)\int e^{(\frac{1}{3}{x}^3+x)}dx+c-e^{(\frac{1}{3}{x}^3+x)}}{c+\int e^{(\frac{1}{3}{x}^3+x)}dx}],\mathtt{\text{riccati}}]$$