8.208   ODE No. 1798

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

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

Mathematica: cpu = 38.092837 (sec), leaf count = 37 $$\text{DSolve}[x^{3}y(x{)}^2{y}^{″}(x)+(y(x)+x){(x{y}^{\prime }(x)-y(x))}^3=0,y(x),x]$$

Maple: cpu = 1.716 (sec), leaf count = 166 $$\{y\left(x\right)=\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-2\ln \left(x\right)-{\int }^{\mathit{\_}\mathit{Z}}1(i\sqrt{3}{\mathit{Y}}_{i\sqrt{3}}\left(2\sqrt{\mathit{\_}\mathit{f}}\right)\mathit{\_}\mathit{C}\mathit{1}\sqrt{\mathit{\_}\mathit{f}}+i\sqrt{3}{\mathit{J}}_{i\sqrt{3}}\left(2\sqrt{\mathit{\_}\mathit{f}}\right)\sqrt{\mathit{\_}\mathit{f}}+{\mathit{Y}}_{i\sqrt{3}}\left(2\sqrt{\mathit{\_}\mathit{f}}\right)\mathit{\_}\mathit{C}\mathit{1}\sqrt{\mathit{\_}\mathit{f}}-2\mathit{\_}\mathit{C}\mathit{1}{\mathit{Y}}_{i\sqrt{3}+1}\left(2\sqrt{\mathit{\_}\mathit{f}}\right)\mathit{\_}\mathit{f}+{\mathit{J}}_{i\sqrt{3}}\left(2\sqrt{\mathit{\_}\mathit{f}}\right)\sqrt{\mathit{\_}\mathit{f}}-2{\mathit{J}}_{i\sqrt{3}+1}\left(2\sqrt{\mathit{\_}\mathit{f}}\right)\mathit{\_}\mathit{f}){\mathit{\_}\mathit{f}}^{-\frac{3}{2}}{({\mathit{Y}}_{i\sqrt{3}}\left(2\sqrt{\mathit{\_}\mathit{f}}\right)\mathit{\_}\mathit{C}\mathit{1}+{\mathit{J}}_{i\sqrt{3}}\left(2\sqrt{\mathit{\_}\mathit{f}}\right))}^{-1}d\mathit{\_}\mathit{f}+2\mathit{\_}\mathit{C}\mathit{2})x\}$$