8.221   ODE No. 1811

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

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

Mathematica: cpu = 0 (sec), leaf count = 0 $$\text{Hanged}$$

Maple: cpu = 3.026 (sec), leaf count = 1864 $$\{y\left(x\right)=\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-\ln \left(x\right)+{\int }^{\mathit{\_}\mathit{Z}}\frac{1}{{\mathit{\_}\mathit{g}}^2+1}(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(\arctan \left(\mathit{\_}\mathit{g}\right)+{\int }^{\mathit{\_}\mathit{Z}}\frac{1}{({\mathit{\_}\mathit{f}}^2{a}^2+a^2-1)({\mathit{\_}\mathit{f}}^2+1)}(1+\sqrt{{\mathit{\_}\mathit{f}}^2{a}^2+a^2})d\mathit{\_}\mathit{f}+\mathit{\_}\mathit{C}\mathit{1})-\mathit{\_}\mathit{g})d\mathit{\_}\mathit{g}+\mathit{\_}\mathit{C}\mathit{2})x,y\left(x\right)=\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(-\ln \left(x\right)+{\int 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