2.1749   ODE No. 1749

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

$$-3y^{\prime }(x{)}^2+4y(x)y^{″}(x)-12y(x{)}^3=0$$ ✓ Mathematica : cpu = 0.457495 (sec), leaf count = 153

$$\{\{y(x)\to \text{InverseFunction}[-\frac{4\mathrm{\#}\text{1}\sqrt{1+\frac{4{\mathrm{\#}\text{1}}^{3/2}}{c_1}}{}_2{F}_1(\frac{1}{6},\frac{1}{2};\frac{7}{6};-\frac{4{\mathrm{\#}\text{1}}^{3/2}}{c_1})}{\sqrt{{\mathrm{\#}\text{1}}^{3/2}(4{\mathrm{\#}\text{1}}^{3/2}+c_1)}}\mathrm{\&}][x+c_2]\},\{y(x)\to \text{InverseFunction}\left[\frac{4\mathrm{\#}\text{1}\sqrt{1+\frac{4{\mathrm{\#}\text{1}}^{3/2}}{c_1}}{}_2{F}_1(\frac{1}{6},\frac{1}{2};\frac{7}{6};-\frac{4{\mathrm{\#}\text{1}}^{3/2}}{c_1})}{\sqrt{{\mathrm{\#}\text{1}}^{3/2}(4{\mathrm{\#}\text{1}}^{3/2}+c_1)}}\mathrm{\&}\right][x+c_2]\}\}$$ ✓ Maple : cpu = 1.408 (sec), leaf count = 57

$$\{{\int }^{y\left(x\right)}\frac{1}{\sqrt{\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{a}}^{\frac{3}{2}}+4{\mathit{\_}\mathit{a}}^3}}d\mathit{\_}\mathit{a}-x-\mathit{\_}\mathit{C}\mathit{2}=0,{\int }^{y\left(x\right)}-\frac{1}{\sqrt{\mathit{\_}\mathit{C}\mathit{1}{\mathit{\_}\mathit{a}}^{\frac{3}{2}}+4{\mathit{\_}\mathit{a}}^3}}d\mathit{\_}\mathit{a}-x-\mathit{\_}\mathit{C}\mathit{2}=0\}$$