3.16   ODE No. 16

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

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

Mathematica: cpu = 21.387216 (sec), leaf count = 24 $$\text{DSolve}[f(x)(xy(x)-1)+y^{\prime }(x)+y(x{)}^2=0,y(x),x]$$

Maple: cpu = 0.093 (sec), leaf count = 50 $$\{y\left(x\right)=-1{\mathrm{e}}^{\int -\frac{x^{2}f\left(x\right)+2}{x}\mathrm{d}x}{(\mathit{\_}\mathit{C}\mathit{1}-\int {\mathrm{e}}^{\int -\frac{x^{2}f\left(x\right)+2}{x}\mathrm{d}x}\mathrm{d}x)}^{-1}+x^{-1}\}$$

Sage: cpu = 0.068 (sec), leaf count = 0 $$[\left[[y\left(x\right)=0,uf\left(x\right)=0]\right],\mathtt{\text{riccati}}]$$