8.188   ODE No. 1778

$$\boxed{{\displaystyle {\left(y\left(x\right)\right)}^2\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)-a=0}}$$

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

Mathematica: cpu = 0.537568 (sec), leaf count = 75 $$\text{Solve}[(\frac{y(x)\sqrt{c_1-\frac{2a}{y(x)}}}{c_1}+\frac{a\log (\sqrt{c_1}y(x)\sqrt{c_1-\frac{2a}{y(x)}}-a+c_{1}y(x))}{c_1^{3/2}}){}^2=(c_2+x){}^2,y(x)]$$

Maple: cpu = 1.950 (sec), leaf count = 369 $$\{y\left(x\right)=\frac{\mathit{\_}\mathit{C}\mathit{1}({\mathit{\_}\mathit{C}\mathit{1}}^2{a}^2+2\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)}+{\left({\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)}\right)}^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}}^2{a}^2+2\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)}+{\left({\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)}\right)}^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)}}\}$$