8.154   ODE No. 1744

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

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

Mathematica: cpu = 0.974624 (sec), leaf count = 173 $$\{\{y(x)\to \text{InverseFunction}[-i{e}^{-c_1}(\sqrt{\mathrm{\#}\text{1}}\sqrt{\mathrm{\#}\text{1}{e}^{2c_1}-1}-e^{-c_1}\log (\sqrt{\mathrm{\#}\text{1}}{e}^{2c_1}+e^{c_1}\sqrt{\mathrm{\#}\text{1}{e}^{2c_1}-1}))\mathrm{\&}][c_2+x]\},\{y(x)\to \text{InverseFunction}\left[i{e}^{-c_1}(\sqrt{\mathrm{\#}\text{1}}\sqrt{\mathrm{\#}\text{1}{e}^{2c_1}-1}-e^{-c_1}\log (\sqrt{\mathrm{\#}\text{1}}{e}^{2c_1}+e^{c_1}\sqrt{\mathrm{\#}\text{1}{e}^{2c_1}-1}))\mathrm{\&}\right][c_2+x]\}\}$$

Maple: cpu = 1.670 (sec), leaf count = 95 $$\{-\frac{\mathit{\_}\mathit{C}\mathit{1}}{2}\arctan \left(1(y\left(x\right)-\frac{\mathit{\_}\mathit{C}\mathit{1}}{2})\frac{1}{\sqrt{\mathit{\_}\mathit{C}\mathit{1}y\left(x\right)-{\left(y\left(x\right)\right)}^2}}\right)-\sqrt{\mathit{\_}\mathit{C}\mathit{1}y\left(x\right)-{\left(y\left(x\right)\right)}^2}-x-\mathit{\_}\mathit{C}\mathit{2}=0,\frac{\mathit{\_}\mathit{C}\mathit{1}}{2}\arctan \left(1(y\left(x\right)-\frac{\mathit{\_}\mathit{C}\mathit{1}}{2})\frac{1}{\sqrt{\mathit{\_}\mathit{C}\mathit{1}y\left(x\right)-{\left(y\left(x\right)\right)}^2}}\right)+\sqrt{\mathit{\_}\mathit{C}\mathit{1}y\left(x\right)-{\left(y\left(x\right)\right)}^2}-x-\mathit{\_}\mathit{C}\mathit{2}=0\}$$