2.1796   ODE No. 1796

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

$$(a^2-x^2)y(x)y^{\prime }(x{)}^2+(a^2-x^2)(a^2-y(x{)}^2)y^{″}(x)-x(a^2-y(x{)}^2)y^{\prime }(x)=0$$ ✓ Mathematica : cpu = 0.241704 (sec), leaf count = 363

$$\{\{y(x)\to -\frac{1}{2}{e}^{-c_2}{(1-\frac{x}{\sqrt{x^2-a^2}})}^{-\frac{c_1}{2}}{(\frac{x}{\sqrt{x^2-a^2}}+1)}^{-\frac{c_1}{2}}\sqrt{2a^2{e}^{2c_2}{(1-\frac{x}{\sqrt{x^2-a^2}})}^{c_1}{(\frac{x}{\sqrt{x^2-a^2}}+1)}^{c_1}-a^2{(\frac{x}{\sqrt{x^2-a^2}}+1)}^{2c_1}-a^2{e}^{4c_2}{(1-\frac{x}{\sqrt{x^2-a^2}})}^{2c_1}}\},\{y(x)\to \frac{1}{2}{e}^{-c_2}{(1-\frac{x}{\sqrt{x^2-a^2}})}^{-\frac{c_1}{2}}{(\frac{x}{\sqrt{x^2-a^2}}+1)}^{-\frac{c_1}{2}}\sqrt{2a^2{e}^{2c_2}{(1-\frac{x}{\sqrt{x^2-a^2}})}^{c_1}{(\frac{x}{\sqrt{x^2-a^2}}+1)}^{c_1}-a^2{(\frac{x}{\sqrt{x^2-a^2}}+1)}^{2c_1}-a^2{e}^{4c_2}{(1-\frac{x}{\sqrt{x^2-a^2}})}^{2c_1}}\}\}$$ ✓ Maple : cpu = 1.084 (sec), leaf count = 51

$$\{y\left(x\right)=\frac{1}{2\mathit{\_}\mathit{C}\mathit{2}}({\left({(x+\sqrt{-a^2+x^2})}^{\mathit{\_}\mathit{C}\mathit{1}}\right)}^2{\mathit{\_}\mathit{C}\mathit{2}}^2+a^2){\left({(x+\sqrt{-a^2+x^2})}^{\mathit{\_}\mathit{C}\mathit{1}}\right)}^{-1}\}$$