9.5   ODE No. 1841

$$\boxed{{\displaystyle x^2\frac{{\mathrm{d}}^3}{\mathrm{d}{x}^3}y\left(x\right)+x\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)+(2xy\left(x\right)-1)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+{\left(y\left(x\right)\right)}^2-f\left(x\right)=0}}$$

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

Mathematica: cpu = 0.087511 (sec), leaf count = 41 $$\text{DSolve}[-f(x)+x^2{y}^{(3)}(x)+x{y}^{″}(x)+(2xy(x)-1)y^{\prime }(x)+y(x{)}^2=0,y(x),x]$$

Maple: cpu = 0.406 (sec), leaf count = 60 $$\{y\left(x\right)=\mathit{O}\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}\mathit{S}\mathit{t}\mathit{r}\mathit{u}\mathit{c}(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right),[\{{\mathit{\_}\mathit{a}}^2\frac{{\mathrm{d}}^2}{\mathrm{d}{\mathit{\_}\mathit{a}}^2}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)+\mathit{\_}\mathit{a}{\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^2-\mathit{\_}\mathit{a}\frac{\mathrm{d}}{\mathrm{d}\mathit{\_}\mathit{a}}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)-\int f\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}=0\},\{\mathit{\_}\mathit{a}=x,\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=y\left(x\right)\},\{x=\mathit{\_}\mathit{a},y\left(x\right)=\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\}])\}$$