8.159   ODE No. 1749

$$\boxed{{\displaystyle 4\left(\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)\right)y\left(x\right)-3{\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^2-12{\left(y\left(x\right)\right)}^3=0}}$$

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

Mathematica: cpu = 0.547069 (sec), leaf count = 181 $$\{\{y(x)\to \text{InverseFunction}[-\frac{4\sqrt{\frac{4{\mathrm{\#}\text{1}}^{3/2}}{c_1}+1}\sqrt{{\mathrm{\#}\text{1}}^{3/2}{c}_1+4{\mathrm{\#}\text{1}}^3}{}_2{F}_1(\frac{1}{6},\frac{1}{2};\frac{7}{6};-\frac{4{\mathrm{\#}\text{1}}^{3/2}}{c_1})}{4{\mathrm{\#}\text{1}}^2+\sqrt{\mathrm{\#}\text{1}}{c}_1}\mathrm{\&}][c_2+x]\},\{y(x)\to \text{InverseFunction}\left[\frac{4\sqrt{\frac{4{\mathrm{\#}\text{1}}^{3/2}}{c_1}+1}\sqrt{{\mathrm{\#}\text{1}}^{3/2}{c}_1+4{\mathrm{\#}\text{1}}^3}{}_2{F}_1(\frac{1}{6},\frac{1}{2};\frac{7}{6};-\frac{4{\mathrm{\#}\text{1}}^{3/2}}{c_1})}{4{\mathrm{\#}\text{1}}^2+\sqrt{\mathrm{\#}\text{1}}{c}_1}\mathrm{\&}\right][c_2+x]\}\}$$

Maple: cpu = 1.684 (sec), leaf count = 57 $$\{{\int }^{y\left(x\right)}\frac{1}{\sqrt{\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{a}}^{\frac{3}{2}}+4{\mathit{\_}\mathit{a}}^3}}d\mathit{\_}\mathit{a}-x-\mathit{\_}\mathit{C}\mathit{2}=0,{\int }^{y\left(x\right)}-\frac{1}{\sqrt{\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{a}}^{\frac{3}{2}}+4{\mathit{\_}\mathit{a}}^3}}d\mathit{\_}\mathit{a}-x-\mathit{\_}\mathit{C}\mathit{2}=0\}$$