8.100   ODE No. 1690

$$\boxed{{\displaystyle \left(\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)\right)\sqrt{x}-{\left(y\left(x\right)\right)}^{3/2}=0}}$$

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

Mathematica: cpu = 22.744388 (sec), leaf count = 25 $$\text{DSolve}[\sqrt{x}{y}^{″}(x)-y(x{)}^{3/2}=0,y(x),x]$$

Maple: cpu = 3.479 (sec), leaf count = 97 $$\{y\left(x\right)=\mathit{O}\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}\mathit{S}\mathit{t}\mathit{r}\mathit{u}\mathit{c}(\frac{\mathit{\_}\mathit{a}}{{\left({\mathrm{e}}^{\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}}\right)}^3},[\{\frac{\mathrm{d}}{\mathrm{d}\mathit{\_}\mathit{a}}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=(-{\mathit{\_}\mathit{a}}^{\frac{3}{2}}+12\mathit{\_}\mathit{a}){\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^3-7{\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^2\},\{\mathit{\_}\mathit{a}=x^{3}y\left(x\right),\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=\frac{1}{x^3(x\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+3y\left(x\right))}\},\{x={\mathrm{e}}^{\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}},y\left(x\right)=\frac{\mathit{\_}\mathit{a}}{{\left({\mathrm{e}}^{\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}}\right)}^3}\}])\}$$