8.209   ODE No. 1799

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

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

Mathematica: cpu = 1.945247 (sec), leaf count = 88 $$\{\{y(x)\to -\frac{\sqrt{a+c_1^2{x}^2+2c_2{c}_1^{2}x+c_2^2{c}_1^2}}{\sqrt{c_1}}\},\{y(x)\to \frac{\sqrt{a+c_1^2{x}^2+2c_2{c}_1^{2}x+c_2^2{c}_1^2}}{\sqrt{c_1}}\}\}$$

Maple: cpu = 1.762 (sec), leaf count = 70 $$\{y\left(x\right)=\frac{1}{\mathit{\_}\mathit{C}\mathit{1}}\sqrt{\mathit{\_}\mathit{C}\mathit{1}({\mathit{\_}\mathit{C}\mathit{1}}^2{\mathit{\_}\mathit{C}\mathit{2}}^2+2{\mathit{\_}\mathit{C}\mathit{1}}^2\mathit{\_}\mathit{C}\mathit{2}x+{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2+a)},y\left(x\right)=-\frac{1}{\mathit{\_}\mathit{C}\mathit{1}}\sqrt{\mathit{\_}\mathit{C}\mathit{1}({\mathit{\_}\mathit{C}\mathit{1}}^2{\mathit{\_}\mathit{C}\mathit{2}}^2+2{\mathit{\_}\mathit{C}\mathit{1}}^2\mathit{\_}\mathit{C}\mathit{2}x+{\mathit{\_}\mathit{C}\mathit{1}}^2{x}^2+a)}\}$$