2.1646   ODE No. 1646

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

$$ay(x){(y^{\prime }(x{)}^2+1)}^2+y^{″}(x)=0$$ ✓ Mathematica : cpu = 10.6045 (sec), leaf count = 262

$$\{\{y(x)\to \text{InverseFunction}[-\frac{\sqrt{\frac{{\mathrm{\#}\text{1}}^2(-a)+1+2c_1}{1+2c_1}}\sqrt{2{\mathrm{\#}\text{1}}^{2}a-4c_1}E({\sin }^{-1}\left(\sqrt{\frac{a}{2c_1+1}}\mathrm{\#}\text{1}\right)|1+\frac{1}{2c_1})}{\sqrt{\frac{a}{1+2c_1}}\sqrt{{\mathrm{\#}\text{1}}^2(-a)+1+2c_1}\sqrt{2-\frac{{\mathrm{\#}\text{1}}^{2}a}{c_1}}}\mathrm{\&}][x+c_2]\},\{y(x)\to \text{InverseFunction}\left[\frac{\sqrt{\frac{{\mathrm{\#}\text{1}}^2(-a)+1+2c_1}{1+2c_1}}\sqrt{2{\mathrm{\#}\text{1}}^{2}a-4c_1}E({\sin }^{-1}\left(\sqrt{\frac{a}{2c_1+1}}\mathrm{\#}\text{1}\right)|1+\frac{1}{2c_1})}{\sqrt{\frac{a}{1+2c_1}}\sqrt{{\mathrm{\#}\text{1}}^2(-a)+1+2c_1}\sqrt{2-\frac{{\mathrm{\#}\text{1}}^{2}a}{c_1}}}\mathrm{\&}\right][x+c_2]\}\}$$ ✓ Maple : cpu = 0.433 (sec), leaf count = 94

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