8.244   ODE No. 1834

$$\boxed{{\displaystyle {({\left(y\left(x\right)\right)}^2-x^2{\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^2+x^{2}y\left(x\right)\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right))}^2-4xy\left(x\right){(x\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)-y\left(x\right))}^3=0}}$$

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

Mathematica: cpu = 16.501095 (sec), leaf count = 53 $$\text{DSolve}[{(x^{2}y(x)y^{″}(x)+x^2(-y^{\prime }(x{)}^2)+y(x{)}^2)}^2-4xy(x){(x{y}^{\prime }(x)-y(x))}^3=0,y(x),x]$$

Maple: cpu = 0.343 (sec), leaf count = 86 $$\{y\left(x\right)=\mathit{O}\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}\mathit{S}\mathit{t}\mathit{r}\mathit{u}\mathit{c}({\mathrm{e}}^{\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}},[\{\frac{\mathrm{d}}{\mathrm{d}\mathit{\_}\mathit{a}}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=2\frac{\sqrt{\mathit{\_}\mathit{a}(\mathit{\_}\mathit{a}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)-1)}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)}{\mathit{\_}\mathit{a}}-\frac{1}{{\mathit{\_}\mathit{a}}^2}(2\sqrt{\mathit{\_}\mathit{a}(\mathit{\_}\mathit{a}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)-1)}+1)\},\{\mathit{\_}\mathit{a}=x,\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=\frac{\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)}{y\left(x\right)}\},\{x=\mathit{\_}\mathit{a},y\left(x\right)={\mathrm{e}}^{\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}}\}])\}$$