2.1745   ODE No. 1745

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

$$2(y(x)-a)y^{″}(x)+y^{\prime }(x{)}^2+1=0$$ ✓ Mathematica : cpu = 0.668804 (sec), leaf count = 251

$$\{\{y(x)\to \text{InverseFunction}[-\frac{2\sqrt{a-\mathrm{\#}\text{1}}(2\mathrm{\#}\text{1}-2a+e^{2c_1})-\sqrt{2}{e}^{3c_1}\sqrt{e^{-2c_1}(2\mathrm{\#}\text{1}-2a+e^{2c_1})}{\sin }^{-1}\left(\sqrt{2}{e}^{-c_1}\sqrt{a-\mathrm{\#}\text{1}}\right)}{2\sqrt{2}\sqrt{2\mathrm{\#}\text{1}-2a+e^{2c_1}}}\mathrm{\&}][x+c_2]\},\{y(x)\to \text{InverseFunction}\left[\frac{2\sqrt{a-\mathrm{\#}\text{1}}(2\mathrm{\#}\text{1}-2a+e^{2c_1})-\sqrt{2}{e}^{3c_1}\sqrt{e^{-2c_1}(2\mathrm{\#}\text{1}-2a+e^{2c_1})}{\sin }^{-1}\left(\sqrt{2}{e}^{-c_1}\sqrt{a-\mathrm{\#}\text{1}}\right)}{2\sqrt{2}\sqrt{2\mathrm{\#}\text{1}-2a+e^{2c_1}}}\mathrm{\&}\right][x+c_2]\}\}$$ ✓ Maple : cpu = 1.424 (sec), leaf count = 117

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