3.65   ODE No. 65

$$\boxed{{\displaystyle \frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)-\sqrt{\frac{{\left(y\left(x\right)\right)}^3+1}{x^3+1}}=0}}$$

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

Mathematica: cpu = 1.550697 (sec), leaf count = 312 $$\left\{\{y(x)\to \text{InverseFunction}\left[\frac{i(\mathrm{\#}\text{1}+1)\sqrt{1+\frac{6i}{(\sqrt{3}-3i)(\mathrm{\#}\text{1}+1)}}\sqrt{\frac{2}{3}-\frac{4i}{(\sqrt{3}+3i)(\mathrm{\#}\text{1}+1)}}F(i{\sinh }^{-1}\left(\frac{\sqrt{-\frac{6i}{3i+\sqrt{3}}}}{\sqrt{\mathrm{\#}\text{1}+1}}\right)|\frac{3i+\sqrt{3}}{3i-\sqrt{3}})}{\sqrt{-\frac{i}{\sqrt{3}+3i}}\sqrt{{\mathrm{\#}\text{1}}^2-\mathrm{\#}\text{1}+1}}\mathrm{\&}\right][c_1+\frac{i(x+1)\sqrt{1+\frac{6i}{(\sqrt{3}-3i)(x+1)}}\sqrt{\frac{2}{3}-\frac{4i}{(\sqrt{3}+3i)(x+1)}}F(i{\sinh }^{-1}\left(\frac{\sqrt{-\frac{6i}{3i+\sqrt{3}}}}{\sqrt{x+1}}\right)|\frac{3i+\sqrt{3}}{3i-\sqrt{3}})}{\sqrt{-\frac{i}{\sqrt{3}+3i}}\sqrt{x^2-x+1}}]\}\right\}$$

Maple: cpu = 0.063 (sec), leaf count = 47 $$\{{\int }^{y\left(x\right)}\frac{1}{\sqrt{{\mathit{\_}\mathit{a}}^3+1}}d\mathit{\_}\mathit{a}+{\int }^x-1\sqrt{\frac{{\left(y\left(x\right)\right)}^3+1}{{\mathit{\_}\mathit{a}}^3+1}}\frac{1}{\sqrt{{\left(y\left(x\right)\right)}^3+1}}d\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}=0\}$$

Sage: cpu = 0 (sec), leaf count = 0 $$\text{Maxima was unable to solve this ODE}$$