2.65   ODE No. 65

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

$$y^{\prime }(x)-\sqrt{\frac{y(x{)}^3+1}{x^3+1}}=0$$ ✓ Mathematica : cpu = 0.961161 (sec), leaf count = 312

$$\left\{\{y(x)\to \text{InverseFunction}\left[\frac{i(\mathrm{\#}\text{1}+1)\sqrt{1+\frac{6i}{(\sqrt{3}-3i)(\mathrm{\#}\text{1}+1)}}\sqrt{\frac{2}{3}-\frac{4i}{(\sqrt{3}+3i)(\mathrm{\#}\text{1}+1)}}F(i{\sinh }^{-1}\left(\frac{\sqrt{-\frac{6i}{3i+\sqrt{3}}}}{\sqrt{\mathrm{\#}\text{1}+1}}\right)|\frac{3i+\sqrt{3}}{3i-\sqrt{3}})}{\sqrt{-\frac{i}{\sqrt{3}+3i}}\sqrt{{\mathrm{\#}\text{1}}^2-\mathrm{\#}\text{1}+1}}\mathrm{\&}\right][\frac{i(x+1)\sqrt{1+\frac{6i}{(\sqrt{3}-3i)(x+1)}}\sqrt{\frac{2}{3}-\frac{4i}{(\sqrt{3}+3i)(x+1)}}F(i{\sinh }^{-1}\left(\frac{\sqrt{-\frac{6i}{3i+\sqrt{3}}}}{\sqrt{x+1}}\right)|\frac{3i+\sqrt{3}}{3i-\sqrt{3}})}{\sqrt{-\frac{i}{\sqrt{3}+3i}}\sqrt{x^2-x+1}}+c_1]\}\right\}$$ ✓ Maple : cpu = 0.044 (sec), leaf count = 47

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