8.206   ODE No. 1796

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

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

Mathematica: cpu = 0.340043 (sec), leaf count = 66 $$\left\{\{y(x)\to \frac{1}{2}{e}^{-c_2}{(\sqrt{x^2-a^2}+x)}^{-c_1}(a^2{(\sqrt{x^2-a^2}+x)}^{2c_1}+e^{2c_2})\}\right\}$$

Maple: cpu = 1.732 (sec), leaf count = 51 $$\{y\left(x\right)=\frac{1}{2\mathit{\_}\mathit{C}\mathit{2}}({\left({(x+\sqrt{-a^2+x^2})}^{\mathit{\_}\mathit{C}\mathit{1}}\right)}^2{\mathit{\_}\mathit{C}\mathit{2}}^2+a^2){\left({(x+\sqrt{-a^2+x^2})}^{\mathit{\_}\mathit{C}\mathit{1}}\right)}^{-1}\}$$