3.15   ODE No. 15

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+{\left(y\left(x\right)\right)}^2-2x^{2}y\left(x\right)+x^4-2x-1=0}}$$

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

Mathematica: cpu = 0.019502 (sec), leaf count = 25 $$\left\{\{y(x)\to \frac{1}{c_1(-e^{2x})-\frac{1}{2}}+x^2+1\}\right\}$$

Maple: cpu = 0.156 (sec), leaf count = 38 $$\{y\left(x\right)=1(\frac{x^2\mathit{\_}\mathit{C}\mathit{1}}{{\left({\mathrm{e}}^x\right)}^2}-x^2-\frac{\mathit{\_}\mathit{C}\mathit{1}}{{\left({\mathrm{e}}^x\right)}^2}-1){(-1+\frac{\mathit{\_}\mathit{C}\mathit{1}}{{\left({\mathrm{e}}^x\right)}^2})}^{-1}\}$$

Sage: cpu = 0.064 (sec), leaf count = 0 $$[[y\left(x\right)=\frac{(c{e}^{\left(2x\right)}+1)x^2+c{e}^{\left(2x\right)}-1}{c{e}^{\left(2x\right)}+1}],\mathtt{\text{riccati}}]$$