8.126   ODE No. 1716

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

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

Mathematica: cpu = 0.645082 (sec), leaf count = 172 $$\{\{y(x)\to \text{InverseFunction}[-\frac{\mathrm{\#}\text{1}\sqrt{1-e^{2c_1}{\mathrm{\#}\text{1}}^{-2a}}{}_2{F}_1(\frac{1}{2},-\frac{1}{2a};1-\frac{1}{2a};e^{2c_1}{\mathrm{\#}\text{1}}^{-2a})}{\sqrt{e^{2c_1}{\mathrm{\#}\text{1}}^{-2a}-1}}\mathrm{\&}][c_2+x]\},\{y(x)\to \text{InverseFunction}\left[\frac{\mathrm{\#}\text{1}\sqrt{1-e^{2c_1}{\mathrm{\#}\text{1}}^{-2a}}{}_2{F}_1(\frac{1}{2},-\frac{1}{2a};1-\frac{1}{2a};e^{2c_1}{\mathrm{\#}\text{1}}^{-2a})}{\sqrt{e^{2c_1}{\mathrm{\#}\text{1}}^{-2a}-1}}\mathrm{\&}\right][c_2+x]\}\}$$

Maple: cpu = 1.622 (sec), leaf count = 68 $$\{{\int }^{y\left(x\right)}\frac{1}{{\mathit{\_}\mathit{a}}^{-a}}\frac{1}{\sqrt{-{\mathit{\_}\mathit{a}}^{2a}+\mathit{\_}\mathit{C}\mathit{1}}}d\mathit{\_}\mathit{a}-x-\mathit{\_}\mathit{C}\mathit{2}=0,{\int }^{y\left(x\right)}-\frac{1}{{\mathit{\_}\mathit{a}}^{-a}}\frac{1}{\sqrt{-{\mathit{\_}\mathit{a}}^{2a}+\mathit{\_}\mathit{C}\mathit{1}}}d\mathit{\_}\mathit{a}-x-\mathit{\_}\mathit{C}\mathit{2}=0\}$$