8.226   ODE No. 1816

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

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

Mathematica: cpu = 63.610077 (sec), leaf count = 34 $$\text{DSolve}[x^2(-y(x))y^{\prime }(x)+y^{\prime }(x)y^{″}(x)-xy(x{)}^2=0,y(x),x]$$

Maple: cpu = 0.874 (sec), leaf count = 46 $$\{y\left(x\right)=\mathit{O}\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}\mathit{S}\mathit{t}\mathit{r}\mathit{u}\mathit{c}(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right),[\{-{\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^2{\mathit{\_}\mathit{a}}^2+{\left(\frac{\mathrm{d}}{\mathrm{d}\mathit{\_}\mathit{a}}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^2+\mathit{\_}\mathit{C}\mathit{1}=0\},\{\mathit{\_}\mathit{a}=x,\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=y\left(x\right)\},\{x=\mathit{\_}\mathit{a},y\left(x\right)=\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\}])\}$$