8.242   ODE No. 1832

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

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

Mathematica: cpu = 0.682087 (sec), leaf count = 24 $$\text{DSolve}[y(x)y^{″}(x{)}^2-a{e}^{2x}=0,y(x),x]$$

Maple: cpu = 0.608 (sec), leaf count = 117 $$\{y\left(x\right)=\mathit{O}\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}\mathit{S}\mathit{t}\mathit{r}\mathit{u}\mathit{c}(\mathit{\_}\mathit{a}{\left({\mathrm{e}}^{-\frac{2\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}}{3}-\frac{2\mathit{\_}\mathit{C}\mathit{1}}{3}}\right)}^{-1},[\{\frac{\mathrm{d}}{\mathrm{d}\mathit{\_}\mathit{a}}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=-\frac{{\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^3}{9\mathit{\_}\mathit{a}}(-4{\mathit{\_}\mathit{a}}^2+9\sqrt{a\mathit{\_}\mathit{a}})+\frac{4{\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^2}{3}\},\{\mathit{\_}\mathit{a}=y\left(x\right){\mathrm{e}}^{-\frac{2x}{3}},\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=-3\frac{1}{{\mathrm{e}}^{-2/3x}(-3\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+2y\left(x\right))}\},\{x=\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1},y\left(x\right)=\mathit{\_}\mathit{a}{\left({\mathrm{e}}^{-\frac{2\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}}{3}-\frac{2\mathit{\_}\mathit{C}\mathit{1}}{3}}\right)}^{-1}\}])\}$$