9.7   ODE No. 1843

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

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

Mathematica: cpu = 2.969877 (sec), leaf count = 409 $$\{\{y(x)\to \text{InverseFunction}[-\frac{2i\sqrt{\frac{{\mathrm{\#}\text{1}}^2}{2(\sqrt{c_2^2-c_1}-c_2)}+1}\sqrt{1-\frac{{\mathrm{\#}\text{1}}^2}{2(c_2+\sqrt{c_2^2-c_1})}}F(i{\sinh }^{-1}\left(\frac{\sqrt{\frac{1}{\sqrt{c_2^2-c_1}-c_2}}\mathrm{\#}\text{1}}{\sqrt{2}}\right)|\frac{c_2-\sqrt{c_2^2-c_1}}{c_2+\sqrt{c_2^2-c_1}})}{\sqrt{\frac{1}{\sqrt{c_2^2-c_1}-c_2}}\sqrt{-\frac{{\mathrm{\#}\text{1}}^4}{2}+2{\mathrm{\#}\text{1}}^2{c}_2-2c_1}}\mathrm{\&}][c_3+x]\},\{y(x)\to \text{InverseFunction}\left[\frac{2i\sqrt{\frac{{\mathrm{\#}\text{1}}^2}{2(\sqrt{c_2^2-c_1}-c_2)}+1}\sqrt{1-\frac{{\mathrm{\#}\text{1}}^2}{2(c_2+\sqrt{c_2^2-c_1})}}F(i{\sinh }^{-1}\left(\frac{\sqrt{\frac{1}{\sqrt{c_2^2-c_1}-c_2}}\mathrm{\#}\text{1}}{\sqrt{2}}\right)|\frac{c_2-\sqrt{c_2^2-c_1}}{c_2+\sqrt{c_2^2-c_1}})}{\sqrt{\frac{1}{\sqrt{c_2^2-c_1}-c_2}}\sqrt{-\frac{{\mathrm{\#}\text{1}}^4}{2}+2{\mathrm{\#}\text{1}}^2{c}_2-2c_1}}\mathrm{\&}\right][c_3+x]\}\}$$

Maple: cpu = 0.234 (sec), leaf count = 77 $$\{{\int }^{y\left(x\right)}-2\frac{1}{\sqrt{-{\mathit{\_}\mathit{a}}^4+4\mathit{\_}\mathit{C}\mathit{2}{\mathit{\_}\mathit{a}}^2-4{\mathit{\_}\mathit{C}\mathit{2}}^2+4\mathit{\_}\mathit{C}\mathit{1}}}d\mathit{\_}\mathit{a}-x-\mathit{\_}\mathit{C}\mathit{3}=0,{\int }^{y\left(x\right)}2\frac{1}{\sqrt{-{\mathit{\_}\mathit{a}}^4+4\mathit{\_}\mathit{C}\mathit{2}{\mathit{\_}\mathit{a}}^2-4{\mathit{\_}\mathit{C}\mathit{2}}^2+4\mathit{\_}\mathit{C}\mathit{1}}}d\mathit{\_}\mathit{a}-x-\mathit{\_}\mathit{C}\mathit{3}=0\}$$