2.1795   ODE No. 1795

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

$$xy(x{)}^2{y}^{″}(x)-a=0$$ ✓ Mathematica : cpu = 0.232431 (sec), leaf count = 116

$$\text{Solve}[-\frac{\sqrt{-\frac{2ay(x)}{x}-\frac{2c_{1}y(x{)}^2}{x^2}}}{2c_1}-\frac{a{\tan }^{-1}\left(\frac{\sqrt{2}\sqrt{c_1}(\frac{y(x)}{x}+\frac{a}{2c_1})}{\sqrt{-\frac{2ay(x)}{x}-\frac{2c_{1}y(x{)}^2}{x^2}}}\right)}{2\sqrt{2}{c}_1{}^{3/2}}-\frac{1}{x}-c_2=0,y(x)]$$ ✓ Maple : cpu = 9.478 (sec), leaf count = 529

$$\{y\left(x\right)=\frac{\mathit{\_}\mathit{C}\mathit{1}{(9\mathit{\_}\mathit{C}\mathit{1}a+{\mathrm{e}}^{\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(243\mathit{c}\mathit{s}\mathit{g}\mathit{n}\left({\mathit{\_}\mathit{C}\mathit{1}}^{-1}\right){\mathit{\_}\mathit{C}\mathit{1}}^4{a}^{2}x-54\mathit{\_}\mathit{Z}{\mathrm{e}}^{\mathit{\_}\mathit{Z}}ax{\mathit{\_}\mathit{C}\mathit{1}}^3-3{\left({\mathrm{e}}^{\mathit{\_}\mathit{Z}}\right)}^2\mathit{c}\mathit{s}\mathit{g}\mathit{n}\left({\mathit{\_}\mathit{C}\mathit{1}}^{-1}\right){\mathit{\_}\mathit{C}\mathit{1}}^{2}x-6{\mathrm{e}}^{\mathit{\_}\mathit{Z}}\mathit{c}\mathit{s}\mathit{g}\mathit{n}\left({\mathit{\_}\mathit{C}\mathit{1}}^{-1}\right)\mathit{\_}\mathit{C}\mathit{2}x-2{\mathrm{e}}^{\mathit{\_}\mathit{Z}}\mathit{c}\mathit{s}\mathit{g}\mathit{n}\left({\mathit{\_}\mathit{C}\mathit{1}}^{-1}\right))})}^{2}x}{2{\mathrm{e}}^{\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(243\mathit{c}\mathit{s}\mathit{g}\mathit{n}\left({\mathit{\_}\mathit{C}\mathit{1}}^{-1}\right){\mathit{\_}\mathit{C}\mathit{1}}^4{a}^{2}x-54\mathit{\_}\mathit{Z}{\mathrm{e}}^{\mathit{\_}\mathit{Z}}ax{\mathit{\_}\mathit{C}\mathit{1}}^3-3{\left({\mathrm{e}}^{\mathit{\_}\mathit{Z}}\right)}^2\mathit{c}\mathit{s}\mathit{g}\mathit{n}\left({\mathit{\_}\mathit{C}\mathit{1}}^{-1}\right){\mathit{\_}\mathit{C}\mathit{1}}^{2}x-6{\mathrm{e}}^{\mathit{\_}\mathit{Z}}\mathit{c}\mathit{s}\mathit{g}\mathit{n}\left({\mathit{\_}\mathit{C}\mathit{1}}^{-1}\right)\mathit{\_}\mathit{C}\mathit{2}x-2{\mathrm{e}}^{\mathit{\_}\mathit{Z}}\mathit{c}\mathit{s}\mathit{g}\mathit{n}\left({\mathit{\_}\mathit{C}\mathit{1}}^{-1}\right))}},y\left(x\right)=\frac{\mathit{\_}\mathit{C}\mathit{1}{(9\mathit{\_}\mathit{C}\mathit{1}a+{\mathrm{e}}^{\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(243\mathit{c}\mathit{s}\mathit{g}\mathit{n}\left({\mathit{\_}\mathit{C}\mathit{1}}^{-1}\right){\mathit{\_}\mathit{C}\mathit{1}}^4{a}^{2}x-54\mathit{\_}\mathit{Z}{\mathrm{e}}^{\mathit{\_}\mathit{Z}}ax{\mathit{\_}\mathit{C}\mathit{1}}^3-3{\left({\mathrm{e}}^{\mathit{\_}\mathit{Z}}\right)}^2\mathit{c}\mathit{s}\mathit{g}\mathit{n}\left({\mathit{\_}\mathit{C}\mathit{1}}^{-1}\right){\mathit{\_}\mathit{C}\mathit{1}}^{2}x+6{\mathrm{e}}^{\mathit{\_}\mathit{Z}}\mathit{c}\mathit{s}\mathit{g}\mathit{n}\left({\mathit{\_}\mathit{C}\mathit{1}}^{-1}\right)\mathit{\_}\mathit{C}\mathit{2}x+2{\mathrm{e}}^{\mathit{\_}\mathit{Z}}\mathit{c}\mathit{s}\mathit{g}\mathit{n}\left({\mathit{\_}\mathit{C}\mathit{1}}^{-1}\right))})}^{2}x}{2{\mathrm{e}}^{\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(243\mathit{c}\mathit{s}\mathit{g}\mathit{n}\left({\mathit{\_}\mathit{C}\mathit{1}}^{-1}\right){\mathit{\_}\mathit{C}\mathit{1}}^4{a}^{2}x-54\mathit{\_}\mathit{Z}{\mathrm{e}}^{\mathit{\_}\mathit{Z}}ax{\mathit{\_}\mathit{C}\mathit{1}}^3-3{\left({\mathrm{e}}^{\mathit{\_}\mathit{Z}}\right)}^2\mathit{c}\mathit{s}\mathit{g}\mathit{n}\left({\mathit{\_}\mathit{C}\mathit{1}}^{-1}\right){\mathit{\_}\mathit{C}\mathit{1}}^{2}x+6{\mathrm{e}}^{\mathit{\_}\mathit{Z}}\mathit{c}\mathit{s}\mathit{g}\mathit{n}\left({\mathit{\_}\mathit{C}\mathit{1}}^{-1}\right)\mathit{\_}\mathit{C}\mathit{2}x+2{\mathrm{e}}^{\mathit{\_}\mathit{Z}}\mathit{c}\mathit{s}\mathit{g}\mathit{n}\left({\mathit{\_}\mathit{C}\mathit{1}}^{-1}\right))}},y\left(x\right)=\frac{\mathit{\_}\mathit{C}\mathit{1}{(9\mathit{\_}\mathit{C}\mathit{1}a+{\mathrm{e}}^{\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(243\mathit{c}\mathit{s}\mathit{g}\mathit{n}\left({\mathit{\_}\mathit{C}\mathit{1}}^{-1}\right){\mathit{\_}\mathit{C}\mathit{1}}^4{a}^{2}x+54\mathit{\_}\mathit{Z}{\mathrm{e}}^{\mathit{\_}\mathit{Z}}ax{\mathit{\_}\mathit{C}\mathit{1}}^3-3{\left({\mathrm{e}}^{\mathit{\_}\mathit{Z}}\right)}^2\mathit{c}\mathit{s}\mathit{g}\mathit{n}\left({\mathit{\_}\mathit{C}\mathit{1}}^{-1}\right){\mathit{\_}\mathit{C}\mathit{1}}^{2}x-6{\mathrm{e}}^{\mathit{\_}\mathit{Z}}\mathit{c}\mathit{s}\mathit{g}\mathit{n}\left({\mathit{\_}\mathit{C}\mathit{1}}^{-1}\right)\mathit{\_}\mathit{C}\mathit{2}x-2{\mathrm{e}}^{\mathit{\_}\mathit{Z}}\mathit{c}\mathit{s}\mathit{g}\mathit{n}\left({\mathit{\_}\mathit{C}\mathit{1}}^{-1}\right))})}^{2}x}{2{\mathrm{e}}^{\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(243\mathit{c}\mathit{s}\mathit{g}\mathit{n}\left({\mathit{\_}\mathit{C}\mathit{1}}^{-1}\right){\mathit{\_}\mathit{C}\mathit{1}}^4{a}^{2}x+54\mathit{\_}\mathit{Z}{\mathrm{e}}^{\mathit{\_}\mathit{Z}}ax{\mathit{\_}\mathit{C}\mathit{1}}^3-3{\left({\mathrm{e}}^{\mathit{\_}\mathit{Z}}\right)}^2\mathit{c}\mathit{s}\mathit{g}\mathit{n}\left({\mathit{\_}\mathit{C}\mathit{1}}^{-1}\right){\mathit{\_}\mathit{C}\mathit{1}}^{2}x-6{\mathrm{e}}^{\mathit{\_}\mathit{Z}}\mathit{c}\mathit{s}\mathit{g}\mathit{n}\left({\mathit{\_}\mathit{C}\mathit{1}}^{-1}\right)\mathit{\_}\mathit{C}\mathit{2}x-2{\mathrm{e}}^{\mathit{\_}\mathit{Z}}\mathit{c}\mathit{s}\mathit{g}\mathit{n}\left({\mathit{\_}\mathit{C}\mathit{1}}^{-1}\right))}},y\left(x\right)=\frac{\mathit{\_}\mathit{C}\mathit{1}{(9\mathit{\_}\mathit{C}\mathit{1}a+{\mathrm{e}}^{\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(243\mathit{c}\mathit{s}\mathit{g}\mathit{n}\left({\mathit{\_}\mathit{C}\mathit{1}}^{-1}\right){\mathit{\_}\mathit{C}\mathit{1}}^4{a}^{2}x+54\mathit{\_}\mathit{Z}{\mathrm{e}}^{\mathit{\_}\mathit{Z}}ax{\mathit{\_}\mathit{C}\mathit{1}}^3-3{\left({\mathrm{e}}^{\mathit{\_}\mathit{Z}}\right)}^2\mathit{c}\mathit{s}\mathit{g}\mathit{n}\left({\mathit{\_}\mathit{C}\mathit{1}}^{-1}\right){\mathit{\_}\mathit{C}\mathit{1}}^{2}x+6{\mathrm{e}}^{\mathit{\_}\mathit{Z}}\mathit{c}\mathit{s}\mathit{g}\mathit{n}\left({\mathit{\_}\mathit{C}\mathit{1}}^{-1}\right)\mathit{\_}\mathit{C}\mathit{2}x+2{\mathrm{e}}^{\mathit{\_}\mathit{Z}}\mathit{c}\mathit{s}\mathit{g}\mathit{n}\left({\mathit{\_}\mathit{C}\mathit{1}}^{-1}\right))})}^{2}x}{2{\mathrm{e}}^{\mathit{R}\mathit{o}\mathit{o}\mathit{t}\mathit{O}\mathit{f}(243\mathit{c}\mathit{s}\mathit{g}\mathit{n}\left({\mathit{\_}\mathit{C}\mathit{1}}^{-1}\right){\mathit{\_}\mathit{C}\mathit{1}}^4{a}^{2}x+54\mathit{\_}\mathit{Z}{\mathrm{e}}^{\mathit{\_}\mathit{Z}}ax{\mathit{\_}\mathit{C}\mathit{1}}^3-3{\left({\mathrm{e}}^{\mathit{\_}\mathit{Z}}\right)}^2\mathit{c}\mathit{s}\mathit{g}\mathit{n}\left({\mathit{\_}\mathit{C}\mathit{1}}^{-1}\right){\mathit{\_}\mathit{C}\mathit{1}}^{2}x+6{\mathrm{e}}^{\mathit{\_}\mathit{Z}}\mathit{c}\mathit{s}\mathit{g}\mathit{n}\left({\mathit{\_}\mathit{C}\mathit{1}}^{-1}\right)\mathit{\_}\mathit{C}\mathit{2}x+2{\mathrm{e}}^{\mathit{\_}\mathit{Z}}\mathit{c}\mathit{s}\mathit{g}\mathit{n}\left({\mathit{\_}\mathit{C}\mathit{1}}^{-1}\right))}}\}$$