8.7   ODE No. 1597

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

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

Mathematica: cpu = 2.336797 (sec), leaf count = 242 $$\{\{y(x)\to -\frac{\sqrt[4]{2}\sqrt{c_1}\sqrt{\frac{i\sqrt{a}}{\sqrt{c_1}}}\text{sn}(\frac{(-1{)}^{3/4}\sqrt{\sqrt{2}\sqrt{a}\sqrt{c_1}{x}^2+2\sqrt{2}\sqrt{a}\sqrt{c_1}{c}_{2}x+\sqrt{2}\sqrt{a}\sqrt{c_1}{c}_2^2}}{\sqrt{2}}|-1)}{\sqrt{a}}\},\{y(x)\to \frac{\sqrt[4]{2}\sqrt{c_1}\sqrt{\frac{i\sqrt{a}}{\sqrt{c_1}}}\text{sn}(\frac{(-1{)}^{3/4}\sqrt{\sqrt{2}\sqrt{a}\sqrt{c_1}{x}^2+2\sqrt{2}\sqrt{a}\sqrt{c_1}{c}_{2}x+\sqrt{2}\sqrt{a}\sqrt{c_1}{c}_2^2}}{\sqrt{2}}|-1)}{\sqrt{a}}\}\}$$

Maple: cpu = 0.031 (sec), leaf count = 21 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{2}\mathit{J}\mathit{a}\mathit{c}\mathit{o}\mathit{b}\mathit{i}\mathit{S}\mathit{N}((\frac{x}{2}\sqrt{-2a}+\mathit{\_}\mathit{C}\mathit{1})\mathit{\_}\mathit{C}\mathit{2},i)\}$$