8.141   ODE No. 1731

$$\boxed{{\displaystyle 2\left(\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)\right)y\left(x\right)-{\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^2-8{\left(y\left(x\right)\right)}^3-4{\left(y\left(x\right)\right)}^2=0}}$$

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

Mathematica: cpu = 1.403178 (sec), leaf count = 359 $$\{\{y(x)\to \text{InverseFunction}[-\frac{2i\mathrm{\#}\text{1}\sqrt{\frac{c_1}{\mathrm{\#}\text{1}(2-2\sqrt{1-c_1})}+1}\sqrt{\frac{c_1}{\mathrm{\#}\text{1}(2\sqrt{1-c_1}+2)}+1}F(i{\sinh }^{-1}\left(\frac{\sqrt{\frac{c_1}{2\sqrt{1-c_1}+2}}}{\sqrt{\mathrm{\#}\text{1}}}\right)|\frac{\sqrt{1-c_1}+1}{1-\sqrt{1-c_1}})}{\sqrt{\frac{c_1}{2\sqrt{1-c_1}+2}}\sqrt{4{\mathrm{\#}\text{1}}^2+4\mathrm{\#}\text{1}+c_1}}\mathrm{\&}][c_2+x]\},\{y(x)\to \text{InverseFunction}\left[\frac{2i\mathrm{\#}\text{1}\sqrt{\frac{c_1}{\mathrm{\#}\text{1}(2-2\sqrt{1-c_1})}+1}\sqrt{\frac{c_1}{\mathrm{\#}\text{1}(2\sqrt{1-c_1}+2)}+1}F(i{\sinh }^{-1}\left(\frac{\sqrt{\frac{c_1}{2\sqrt{1-c_1}+2}}}{\sqrt{\mathrm{\#}\text{1}}}\right)|\frac{\sqrt{1-c_1}+1}{1-\sqrt{1-c_1}})}{\sqrt{\frac{c_1}{2\sqrt{1-c_1}+2}}\sqrt{4{\mathrm{\#}\text{1}}^2+4\mathrm{\#}\text{1}+c_1}}\mathrm{\&}\right][c_2+x]\}\}$$

Maple: cpu = 1.653 (sec), leaf count = 63 $$\{{\int }^{y\left(x\right)}\frac{1}{\sqrt{4{\mathit{\_}\mathit{a}}^3+\mathit{\_}\mathit{a}\mathit{\_}\mathit{C}\mathit{1}+4{\mathit{\_}\mathit{a}}^2}}d\mathit{\_}\mathit{a}-x-\mathit{\_}\mathit{C}\mathit{2}=0,{\int }^{y\left(x\right)}-\frac{1}{\sqrt{4{\mathit{\_}\mathit{a}}^3+\mathit{\_}\mathit{a}\mathit{\_}\mathit{C}\mathit{1}+4{\mathit{\_}\mathit{a}}^2}}d\mathit{\_}\mathit{a}-x-\mathit{\_}\mathit{C}\mathit{2}=0\}$$