8.137   ODE No. 1727

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

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

Mathematica: cpu = 0.172522 (sec), leaf count = 129 $$\{\{y(x)\to \text{InverseFunction}[e^{2c_1}{\tan }^{-1}\left(\frac{\sqrt{\mathrm{\#}\text{1}}}{\sqrt{e^{2c_1}-\mathrm{\#}\text{1}}}\right)-\sqrt{\mathrm{\#}\text{1}}\sqrt{e^{2c_1}-\mathrm{\#}\text{1}}\mathrm{\&}][c_2+x]\},\{y(x)\to \text{InverseFunction}[\sqrt{\mathrm{\#}\text{1}}\sqrt{e^{2c_1}-\mathrm{\#}\text{1}}-e^{2c_1}{\tan }^{-1}\left(\frac{\sqrt{\mathrm{\#}\text{1}}}{\sqrt{e^{2c_1}-\mathrm{\#}\text{1}}}\right)\mathrm{\&}][c_2+x]\}\}$$

Maple: cpu = 1.716 (sec), leaf count = 95 $$\{-\sqrt{\mathit{\_}\mathit{C}\mathit{1}y\left(x\right)-{\left(y\left(x\right)\right)}^2}+\frac{\mathit{\_}\mathit{C}\mathit{1}}{2}\arctan \left(1(y\left(x\right)-\frac{\mathit{\_}\mathit{C}\mathit{1}}{2})\frac{1}{\sqrt{\mathit{\_}\mathit{C}\mathit{1}y\left(x\right)-{\left(y\left(x\right)\right)}^2}}\right)-x-\mathit{\_}\mathit{C}\mathit{2}=0,\sqrt{\mathit{\_}\mathit{C}\mathit{1}y\left(x\right)-{\left(y\left(x\right)\right)}^2}-\frac{\mathit{\_}\mathit{C}\mathit{1}}{2}\arctan \left(1(y\left(x\right)-\frac{\mathit{\_}\mathit{C}\mathit{1}}{2})\frac{1}{\sqrt{\mathit{\_}\mathit{C}\mathit{1}y\left(x\right)-{\left(y\left(x\right)\right)}^2}}\right)-x-\mathit{\_}\mathit{C}\mathit{2}=0\}$$