2.1778   ODE No. 1778

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

$$y(x{)}^2{y}^{″}(x)-a=0$$ ✓ Mathematica : cpu = 0.183982 (sec), leaf count = 65

$$\text{Solve}[(\frac{y(x)\sqrt{-\frac{2a}{y(x)}+c_1}}{c_1}+\frac{2a{\tanh }^{-1}\left(\frac{\sqrt{-\frac{2a}{y(x)}+c_1}}{\sqrt{c_1}}\right)}{c_1{}^{3/2}}){}^2=(x+c_2){}^2,y(x)]$$ ✓ Maple : cpu = 4.185 (sec), leaf count = 245

$$\{y\left(x\right)=\frac{\mathit{\_}\mathit{C}\mathit{1}{(\mathit{\_}\mathit{C}\mathit{1}a+{\mathrm{e}}^{\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(\mathit{c}\mathit{s}\mathit{g}\mathit{n}\left({\mathit{\_}\mathit{C}\mathit{1}}^{-1}\right){\mathit{\_}\mathit{C}\mathit{1}}^4{a}^2-2\mathit{\_}\mathit{Z}{\mathit{\_}\mathit{C}\mathit{1}}^{3}a{\mathrm{e}}^{\mathit{\_}\mathit{Z}}-\mathit{c}\mathit{s}\mathit{g}\mathit{n}\left({\mathit{\_}\mathit{C}\mathit{1}}^{-1}\right){\left({\mathrm{e}}^{\mathit{\_}\mathit{Z}}\right)}^2{\mathit{\_}\mathit{C}\mathit{1}}^2-2\mathit{c}\mathit{s}\mathit{g}\mathit{n}\left({\mathit{\_}\mathit{C}\mathit{1}}^{-1}\right){\mathrm{e}}^{\mathit{\_}\mathit{Z}}\mathit{\_}\mathit{C}\mathit{2}-2\mathit{c}\mathit{s}\mathit{g}\mathit{n}\left({\mathit{\_}\mathit{C}\mathit{1}}^{-1}\right){\mathrm{e}}^{\mathit{\_}\mathit{Z}}x)})}^2}{2{\mathrm{e}}^{\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(\mathit{c}\mathit{s}\mathit{g}\mathit{n}\left({\mathit{\_}\mathit{C}\mathit{1}}^{-1}\right){\mathit{\_}\mathit{C}\mathit{1}}^4{a}^2-2\mathit{\_}\mathit{Z}{\mathit{\_}\mathit{C}\mathit{1}}^{3}a{\mathrm{e}}^{\mathit{\_}\mathit{Z}}-\mathit{c}\mathit{s}\mathit{g}\mathit{n}\left({\mathit{\_}\mathit{C}\mathit{1}}^{-1}\right){\left({\mathrm{e}}^{\mathit{\_}\mathit{Z}}\right)}^2{\mathit{\_}\mathit{C}\mathit{1}}^2-2\mathit{c}\mathit{s}\mathit{g}\mathit{n}\left({\mathit{\_}\mathit{C}\mathit{1}}^{-1}\right){\mathrm{e}}^{\mathit{\_}\mathit{Z}}\mathit{\_}\mathit{C}\mathit{2}-2\mathit{c}\mathit{s}\mathit{g}\mathit{n}\left({\mathit{\_}\mathit{C}\mathit{1}}^{-1}\right){\mathrm{e}}^{\mathit{\_}\mathit{Z}}x)}},y\left(x\right)=\frac{\mathit{\_}\mathit{C}\mathit{1}{(\mathit{\_}\mathit{C}\mathit{1}a+{\mathrm{e}}^{\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(\mathit{c}\mathit{s}\mathit{g}\mathit{n}\left({\mathit{\_}\mathit{C}\mathit{1}}^{-1}\right){\mathit{\_}\mathit{C}\mathit{1}}^4{a}^2-2\mathit{\_}\mathit{Z}{\mathit{\_}\mathit{C}\mathit{1}}^{3}a{\mathrm{e}}^{\mathit{\_}\mathit{Z}}-\mathit{c}\mathit{s}\mathit{g}\mathit{n}\left({\mathit{\_}\mathit{C}\mathit{1}}^{-1}\right){\left({\mathrm{e}}^{\mathit{\_}\mathit{Z}}\right)}^2{\mathit{\_}\mathit{C}\mathit{1}}^2+2\mathit{c}\mathit{s}\mathit{g}\mathit{n}\left({\mathit{\_}\mathit{C}\mathit{1}}^{-1}\right){\mathrm{e}}^{\mathit{\_}\mathit{Z}}\mathit{\_}\mathit{C}\mathit{2}+2\mathit{c}\mathit{s}\mathit{g}\mathit{n}\left({\mathit{\_}\mathit{C}\mathit{1}}^{-1}\right){\mathrm{e}}^{\mathit{\_}\mathit{Z}}x)})}^2}{2{\mathrm{e}}^{\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(\mathit{c}\mathit{s}\mathit{g}\mathit{n}\left({\mathit{\_}\mathit{C}\mathit{1}}^{-1}\right){\mathit{\_}\mathit{C}\mathit{1}}^4{a}^2-2\mathit{\_}\mathit{Z}{\mathit{\_}\mathit{C}\mathit{1}}^{3}a{\mathrm{e}}^{\mathit{\_}\mathit{Z}}-\mathit{c}\mathit{s}\mathit{g}\mathit{n}\left({\mathit{\_}\mathit{C}\mathit{1}}^{-1}\right){\left({\mathrm{e}}^{\mathit{\_}\mathit{Z}}\right)}^2{\mathit{\_}\mathit{C}\mathit{1}}^2+2\mathit{c}\mathit{s}\mathit{g}\mathit{n}\left({\mathit{\_}\mathit{C}\mathit{1}}^{-1}\right){\mathrm{e}}^{\mathit{\_}\mathit{Z}}\mathit{\_}\mathit{C}\mathit{2}+2\mathit{c}\mathit{s}\mathit{g}\mathit{n}\left({\mathit{\_}\mathit{C}\mathit{1}}^{-1}\right){\mathrm{e}}^{\mathit{\_}\mathit{Z}}x)}}\}$$