2.1727   ODE No. 1727

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

$$y^{\prime }(x{)}^2+2y(x)y^{″}(x)+1=0$$ ✓ Mathematica : cpu = 0.346165 (sec), leaf count = 166

$$\{\{y(x)\to \text{InverseFunction}[-\frac{\sqrt{\mathrm{\#}\text{1}}(\mathrm{\#}\text{1}-e^{2c_1})+e^{3c_1}\sqrt{1-\mathrm{\#}\text{1}{e}^{-2c_1}}{\sin }^{-1}\left(\sqrt{\mathrm{\#}\text{1}}{e}^{-c_1}\right)}{\sqrt{-\mathrm{\#}\text{1}+e^{2c_1}}}\mathrm{\&}][x+c_2]\},\{y(x)\to \text{InverseFunction}\left[\frac{\sqrt{\mathrm{\#}\text{1}}(\mathrm{\#}\text{1}-e^{2c_1})+e^{3c_1}\sqrt{1-\mathrm{\#}\text{1}{e}^{-2c_1}}{\sin }^{-1}\left(\sqrt{\mathrm{\#}\text{1}}{e}^{-c_1}\right)}{\sqrt{-\mathrm{\#}\text{1}+e^{2c_1}}}\mathrm{\&}\right][x+c_2]\}\}$$ ✓ Maple : cpu = 1.069 (sec), leaf count = 823

$$\{y\left(x\right)=\frac{\tan \left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}({(\tan \left(\mathit{\_}\mathit{Z}\right))}^2{\mathit{\_}\mathit{C}\mathit{1}}^2{\mathit{\_}\mathit{Z}}^2-4{(\tan \left(\mathit{\_}\mathit{Z}\right))}^2\mathit{\_}\mathit{C}\mathit{1}\mathit{\_}\mathit{C}\mathit{2}\mathit{\_}\mathit{Z}-4{(\tan \left(\mathit{\_}\mathit{Z}\right))}^2\mathit{\_}\mathit{C}\mathit{1}x\mathit{\_}\mathit{Z}+4{(\tan \left(\mathit{\_}\mathit{Z}\right))}^2{\mathit{\_}\mathit{C}\mathit{2}}^2+8{(\tan \left(\mathit{\_}\mathit{Z}\right))}^{2}x\mathit{\_}\mathit{C}\mathit{2}+4{(\tan \left(\mathit{\_}\mathit{Z}\right))}^2{x}^2+{\mathit{\_}\mathit{C}\mathit{1}}^2{\mathit{\_}\mathit{Z}}^2-4\mathit{\_}\mathit{C}\mathit{1}\mathit{\_}\mathit{Z}\mathit{\_}\mathit{C}\mathit{2}-4\mathit{\_}\mathit{C}\mathit{1}x\mathit{\_}\mathit{Z}-{\mathit{\_}\mathit{C}\mathit{1}}^2+4{\mathit{\_}\mathit{C}\mathit{2}}^2+8\mathit{\_}\mathit{C}\mathit{2}x+4x^2)\right)(-\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}({(\tan \left(\mathit{\_}\mathit{Z}\right))}^2{\mathit{\_}\mathit{C}\mathit{1}}^2{\mathit{\_}\mathit{Z}}^2-4{(\tan \left(\mathit{\_}\mathit{Z}\right))}^2\mathit{\_}\mathit{C}\mathit{1}\mathit{\_}\mathit{C}\mathit{2}\mathit{\_}\mathit{Z}-4{(\tan \left(\mathit{\_}\mathit{Z}\right))}^2\mathit{\_}\mathit{C}\mathit{1}x\mathit{\_}\mathit{Z}+4{(\tan \left(\mathit{\_}\mathit{Z}\right))}^2{\mathit{\_}\mathit{C}\mathit{2}}^2+8{(\tan \left(\mathit{\_}\mathit{Z}\right))}^{2}x\mathit{\_}\mathit{C}\mathit{2}+4{(\tan \left(\mathit{\_}\mathit{Z}\right))}^2{x}^2+{\mathit{\_}\mathit{C}\mathit{1}}^2{\mathit{\_}\mathit{Z}}^2-4\mathit{\_}\mathit{C}\mathit{1}\mathit{\_}\mathit{Z}\mathit{\_}\mathit{C}\mathit{2}-4\mathit{\_}\mathit{C}\mathit{1}x\mathit{\_}\mathit{Z}-{\mathit{\_}\mathit{C}\mathit{1}}^2+4{\mathit{\_}\mathit{C}\mathit{2}}^2+8\mathit{\_}\mathit{C}\mathit{2}x+4x^2)\mathit{\_}\mathit{C}\mathit{1}+2\mathit{\_}\mathit{C}\mathit{2}+2x)}{2}+\frac{\mathit{\_}\mathit{C}\mathit{1}}{2},y\left(x\right)=\frac{\tan \left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}({(\tan \left(\mathit{\_}\mathit{Z}\right))}^2{\mathit{\_}\mathit{C}\mathit{1}}^2{\mathit{\_}\mathit{Z}}^2-4{(\tan \left(\mathit{\_}\mathit{Z}\right))}^2\mathit{\_}\mathit{C}\mathit{1}\mathit{\_}\mathit{C}\mathit{2}\mathit{\_}\mathit{Z}-4{(\tan \left(\mathit{\_}\mathit{Z}\right))}^2\mathit{\_}\mathit{C}\mathit{1}x\mathit{\_}\mathit{Z}+4{(\tan \left(\mathit{\_}\mathit{Z}\right))}^2{\mathit{\_}\mathit{C}\mathit{2}}^2+8{(\tan \left(\mathit{\_}\mathit{Z}\right))}^{2}x\mathit{\_}\mathit{C}\mathit{2}+4{(\tan \left(\mathit{\_}\mathit{Z}\right))}^2{x}^2+{\mathit{\_}\mathit{C}\mathit{1}}^2{\mathit{\_}\mathit{Z}}^2-4\mathit{\_}\mathit{C}\mathit{1}\mathit{\_}\mathit{Z}\mathit{\_}\mathit{C}\mathit{2}-4\mathit{\_}\mathit{C}\mathit{1}x\mathit{\_}\mathit{Z}-{\mathit{\_}\mathit{C}\mathit{1}}^2+4{\mathit{\_}\mathit{C}\mathit{2}}^2+8\mathit{\_}\mathit{C}\mathit{2}x+4x^2)\right)(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}({(\tan \left(\mathit{\_}\mathit{Z}\right))}^2{\mathit{\_}\mathit{C}\mathit{1}}^2{\mathit{\_}\mathit{Z}}^2-4{(\tan \left(\mathit{\_}\mathit{Z}\right))}^2\mathit{\_}\mathit{C}\mathit{1}\mathit{\_}\mathit{C}\mathit{2}\mathit{\_}\mathit{Z}-4{(\tan \left(\mathit{\_}\mathit{Z}\right))}^2\mathit{\_}\mathit{C}\mathit{1}x\mathit{\_}\mathit{Z}+4{(\tan \left(\mathit{\_}\mathit{Z}\right))}^2{\mathit{\_}\mathit{C}\mathit{2}}^2+8{(\tan \left(\mathit{\_}\mathit{Z}\right))}^{2}x\mathit{\_}\mathit{C}\mathit{2}+4{(\tan \left(\mathit{\_}\mathit{Z}\right))}^2{x}^2+{\mathit{\_}\mathit{C}\mathit{1}}^2{\mathit{\_}\mathit{Z}}^2-4\mathit{\_}\mathit{C}\mathit{1}\mathit{\_}\mathit{Z}\mathit{\_}\mathit{C}\mathit{2}-4\mathit{\_}\mathit{C}\mathit{1}x\mathit{\_}\mathit{Z}-{\mathit{\_}\mathit{C}\mathit{1}}^2+4{\mathit{\_}\mathit{C}\mathit{2}}^2+8\mathit{\_}\mathit{C}\mathit{2}x+4x^2)\mathit{\_}\mathit{C}\mathit{1}-2\mathit{\_}\mathit{C}\mathit{2}-2x)}{2}+\frac{\mathit{\_}\mathit{C}\mathit{1}}{2},y\left(x\right)=\frac{\tan \left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}({(\tan \left(\mathit{\_}\mathit{Z}\right))}^2{\mathit{\_}\mathit{C}\mathit{1}}^2{\mathit{\_}\mathit{Z}}^2+4{(\tan \left(\mathit{\_}\mathit{Z}\right))}^2\mathit{\_}\mathit{C}\mathit{1}\mathit{\_}\mathit{C}\mathit{2}\mathit{\_}\mathit{Z}+4{(\tan \left(\mathit{\_}\mathit{Z}\right))}^2\mathit{\_}\mathit{C}\mathit{1}x\mathit{\_}\mathit{Z}+4{(\tan \left(\mathit{\_}\mathit{Z}\right))}^2{\mathit{\_}\mathit{C}\mathit{2}}^2+8{(\tan \left(\mathit{\_}\mathit{Z}\right))}^{2}x\mathit{\_}\mathit{C}\mathit{2}+4{(\tan \left(\mathit{\_}\mathit{Z}\right))}^2{x}^2+{\mathit{\_}\mathit{C}\mathit{1}}^2{\mathit{\_}\mathit{Z}}^2+4\mathit{\_}\mathit{C}\mathit{1}\mathit{\_}\mathit{Z}\mathit{\_}\mathit{C}\mathit{2}+4\mathit{\_}\mathit{C}\mathit{1}x\mathit{\_}\mathit{Z}-{\mathit{\_}\mathit{C}\mathit{1}}^2+4{\mathit{\_}\mathit{C}\mathit{2}}^2+8\mathit{\_}\mathit{C}\mathit{2}x+4x^2)\right)(-\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}({(\tan \left(\mathit{\_}\mathit{Z}\right))}^2{\mathit{\_}\mathit{C}\mathit{1}}^2{\mathit{\_}\mathit{Z}}^2+4{(\tan \left(\mathit{\_}\mathit{Z}\right))}^2\mathit{\_}\mathit{C}\mathit{1}\mathit{\_}\mathit{C}\mathit{2}\mathit{\_}\mathit{Z}+4{(\tan \left(\mathit{\_}\mathit{Z}\right))}^2\mathit{\_}\mathit{C}\mathit{1}x\mathit{\_}\mathit{Z}+4{(\tan \left(\mathit{\_}\mathit{Z}\right))}^2{\mathit{\_}\mathit{C}\mathit{2}}^2+8{(\tan \left(\mathit{\_}\mathit{Z}\right))}^{2}x\mathit{\_}\mathit{C}\mathit{2}+4{(\tan \left(\mathit{\_}\mathit{Z}\right))}^2{x}^2+{\mathit{\_}\mathit{C}\mathit{1}}^2{\mathit{\_}\mathit{Z}}^2+4\mathit{\_}\mathit{C}\mathit{1}\mathit{\_}\mathit{Z}\mathit{\_}\mathit{C}\mathit{2}+4\mathit{\_}\mathit{C}\mathit{1}x\mathit{\_}\mathit{Z}-{\mathit{\_}\mathit{C}\mathit{1}}^2+4{\mathit{\_}\mathit{C}\mathit{2}}^2+8\mathit{\_}\mathit{C}\mathit{2}x+4x^2)\mathit{\_}\mathit{C}\mathit{1}-2\mathit{\_}\mathit{C}\mathit{2}-2x)}{2}+\frac{\mathit{\_}\mathit{C}\mathit{1}}{2},y\left(x\right)=\frac{\tan \left(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}({(\tan \left(\mathit{\_}\mathit{Z}\right))}^2{\mathit{\_}\mathit{C}\mathit{1}}^2{\mathit{\_}\mathit{Z}}^2+4{(\tan \left(\mathit{\_}\mathit{Z}\right))}^2\mathit{\_}\mathit{C}\mathit{1}\mathit{\_}\mathit{C}\mathit{2}\mathit{\_}\mathit{Z}+4{(\tan \left(\mathit{\_}\mathit{Z}\right))}^2\mathit{\_}\mathit{C}\mathit{1}x\mathit{\_}\mathit{Z}+4{(\tan \left(\mathit{\_}\mathit{Z}\right))}^2{\mathit{\_}\mathit{C}\mathit{2}}^2+8{(\tan \left(\mathit{\_}\mathit{Z}\right))}^{2}x\mathit{\_}\mathit{C}\mathit{2}+4{(\tan \left(\mathit{\_}\mathit{Z}\right))}^2{x}^2+{\mathit{\_}\mathit{C}\mathit{1}}^2{\mathit{\_}\mathit{Z}}^2+4\mathit{\_}\mathit{C}\mathit{1}\mathit{\_}\mathit{Z}\mathit{\_}\mathit{C}\mathit{2}+4\mathit{\_}\mathit{C}\mathit{1}x\mathit{\_}\mathit{Z}-{\mathit{\_}\mathit{C}\mathit{1}}^2+4{\mathit{\_}\mathit{C}\mathit{2}}^2+8\mathit{\_}\mathit{C}\mathit{2}x+4x^2)\right)(\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}({(\tan \left(\mathit{\_}\mathit{Z}\right))}^2{\mathit{\_}\mathit{C}\mathit{1}}^2{\mathit{\_}\mathit{Z}}^2+4{(\tan \left(\mathit{\_}\mathit{Z}\right))}^2\mathit{\_}\mathit{C}\mathit{1}\mathit{\_}\mathit{C}\mathit{2}\mathit{\_}\mathit{Z}+4{(\tan \left(\mathit{\_}\mathit{Z}\right))}^2\mathit{\_}\mathit{C}\mathit{1}x\mathit{\_}\mathit{Z}+4{(\tan \left(\mathit{\_}\mathit{Z}\right))}^2{\mathit{\_}\mathit{C}\mathit{2}}^2+8{(\tan \left(\mathit{\_}\mathit{Z}\right))}^{2}x\mathit{\_}\mathit{C}\mathit{2}+4{(\tan \left(\mathit{\_}\mathit{Z}\right))}^2{x}^2+{\mathit{\_}\mathit{C}\mathit{1}}^2{\mathit{\_}\mathit{Z}}^2+4\mathit{\_}\mathit{C}\mathit{1}\mathit{\_}\mathit{Z}\mathit{\_}\mathit{C}\mathit{2}+4\mathit{\_}\mathit{C}\mathit{1}x\mathit{\_}\mathit{Z}-{\mathit{\_}\mathit{C}\mathit{1}}^2+4{\mathit{\_}\mathit{C}\mathit{2}}^2+8\mathit{\_}\mathit{C}\mathit{2}x+4x^2)\mathit{\_}\mathit{C}\mathit{1}+2\mathit{\_}\mathit{C}\mathit{2}+2x)}{2}+\frac{\mathit{\_}\mathit{C}\mathit{1}}{2}\}$$