2.1716   ODE No. 1716

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

$$a(y^{\prime }(x{)}^2+1)+y(x)y^{″}(x)=0$$ ✓ Mathematica : cpu = 0.525633 (sec), leaf count = 172

$$\{\{y(x)\to \text{InverseFunction}[-\frac{\mathrm{\#}\text{1}\sqrt{1-e^{2c_1}{\mathrm{\#}\text{1}}^{-2a}}{}_2{F}_1(\frac{1}{2},-\frac{1}{2a};1-\frac{1}{2a};e^{2c_1}{\mathrm{\#}\text{1}}^{-2a})}{\sqrt{-1+e^{2c_1}{\mathrm{\#}\text{1}}^{-2a}}}\mathrm{\&}][x+c_2]\},\{y(x)\to \text{InverseFunction}\left[\frac{\mathrm{\#}\text{1}\sqrt{1-e^{2c_1}{\mathrm{\#}\text{1}}^{-2a}}{}_2{F}_1(\frac{1}{2},-\frac{1}{2a};1-\frac{1}{2a};e^{2c_1}{\mathrm{\#}\text{1}}^{-2a})}{\sqrt{-1+e^{2c_1}{\mathrm{\#}\text{1}}^{-2a}}}\mathrm{\&}\right][x+c_2]\}\}$$ ✓ Maple : cpu = 1.245 (sec), leaf count = 68

$$\{{\int }^{y\left(x\right)}\frac{1}{{\mathit{\_}\mathit{a}}^{-a}}\frac{1}{\sqrt{-{\mathit{\_}\mathit{a}}^{2a}+\mathit{\_}\mathit{C}\mathit{1}}}d\mathit{\_}\mathit{a}-x-\mathit{\_}\mathit{C}\mathit{2}=0,{\int }^{y\left(x\right)}-\frac{1}{{\mathit{\_}\mathit{a}}^{-a}}\frac{1}{\sqrt{-{\mathit{\_}\mathit{a}}^{2a}+\mathit{\_}\mathit{C}\mathit{1}}}d\mathit{\_}\mathit{a}-x-\mathit{\_}\mathit{C}\mathit{2}=0\}$$