8.140   ODE No. 1730

$$\boxed{{\displaystyle 2\left(\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)\right)y\left(x\right)-{\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^2-8{\left(y\left(x\right)\right)}^3=0}}$$

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

Mathematica: cpu = 0.483061 (sec), leaf count = 127 $$\{\{y(x)\to -\frac{1}{2}i\sqrt{c_1}\text{ns}(\frac{1}{2}(-(-1{)}^{3/4}\sqrt{2}\sqrt[4]{c_1}x-(-1{)}^{3/4}\sqrt{2}\sqrt[4]{c_1}{c}_2)|-1){}^2\},\{y(x)\to -\frac{1}{2}i\sqrt{c_1}\text{ns}(\frac{1}{2}((-1{)}^{3/4}\sqrt{2}\sqrt[4]{c_1}x+(-1{)}^{3/4}\sqrt{2}\sqrt[4]{c_1}{c}_2)|-1){}^2\}\}$$

Maple: cpu = 1.669 (sec), leaf count = 53 $$\{{\int }^{y\left(x\right)}\frac{1}{\sqrt{4{\mathit{\_}\mathit{a}}^3+\mathit{\_}\mathit{C}\mathit{1}\mathit{\_}\mathit{a}}}d\mathit{\_}\mathit{a}-x-\mathit{\_}\mathit{C}\mathit{2}=0,{\int }^{y\left(x\right)}-\frac{1}{\sqrt{4{\mathit{\_}\mathit{a}}^3+\mathit{\_}\mathit{C}\mathit{1}\mathit{\_}\mathit{a}}}d\mathit{\_}\mathit{a}-x-\mathit{\_}\mathit{C}\mathit{2}=0\}$$