8.15   ODE No. 1605

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

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

Mathematica: cpu = 0.519566 (sec), leaf count = 22 $$\text{DSolve}[a{e}^x\sqrt{y(x)}+y^{″}(x)=0,y(x),x]$$

Maple: cpu = 0.811 (sec), leaf count = 109 $$\{y\left(x\right)=\mathit{O}\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}\mathit{S}\mathit{t}\mathit{r}\mathit{u}\mathit{c}(\frac{\mathit{\_}\mathit{a}}{{\mathrm{e}}^{-2\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}-2\mathit{\_}\mathit{C}\mathit{1}}},[\{\frac{\mathrm{d}}{\mathrm{d}\mathit{\_}\mathit{a}}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=(\sqrt{\mathit{\_}\mathit{a}}a+4\mathit{\_}\mathit{a}){\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^3+4{\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^2\},\{\mathit{\_}\mathit{a}=y\left(x\right){\mathrm{e}}^{-2x},\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=-\frac{1}{{\mathrm{e}}^{-2x}(2y\left(x\right)-\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right))}\},\{x=\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1},y\left(x\right)=\frac{\mathit{\_}\mathit{a}}{{\mathrm{e}}^{-2\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}-2\mathit{\_}\mathit{C}\mathit{1}}}\}])\}$$