2.1620   ODE No. 1620

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

$$y^{″}(x)+y(x)y^{\prime }(x)-y(x{)}^3=0$$ ✗ Mathematica : cpu = 122.262 (sec), leaf count = 0 , could not solve

DSolve[-y[x]^3 + y[x]*Derivative[1][y][x] + Derivative[2][y][x] == 0, y[x], x]

✓ Maple : cpu = 0.127 (sec), leaf count = 253

$$\{{\int }^{y\left(x\right)}{(\frac{{\mathit{\_}\mathit{a}}^2}{2}+\frac{1}{2}{(\sqrt[3]{\mathit{\_}\mathit{C}\mathit{1}+\sqrt{{\mathit{\_}\mathit{a}}^6+{\mathit{\_}\mathit{C}\mathit{1}}^2}}-{\mathit{\_}\mathit{a}}^2\frac{1}{\sqrt[3]{\mathit{\_}\mathit{C}\mathit{1}+\sqrt{{\mathit{\_}\mathit{a}}^6+{\mathit{\_}\mathit{C}\mathit{1}}^2}}})}^2)}^{-1}d\mathit{\_}\mathit{a}-x-\mathit{\_}\mathit{C}\mathit{2}=0,{\int }^{y\left(x\right)}{(\frac{{\mathit{\_}\mathit{a}}^2}{2}+\frac{1}{2}{(-\frac{1}{2}\sqrt[3]{\mathit{\_}\mathit{C}\mathit{1}+\sqrt{{\mathit{\_}\mathit{a}}^6+{\mathit{\_}\mathit{C}\mathit{1}}^2}}+\frac{{\mathit{\_}\mathit{a}}^2}{2}\frac{1}{\sqrt[3]{\mathit{\_}\mathit{C}\mathit{1}+\sqrt{{\mathit{\_}\mathit{a}}^6+{\mathit{\_}\mathit{C}\mathit{1}}^2}}}-\frac{i}{2}\sqrt{3}(\sqrt[3]{\mathit{\_}\mathit{C}\mathit{1}+\sqrt{{\mathit{\_}\mathit{a}}^6+{\mathit{\_}\mathit{C}\mathit{1}}^2}}+{\mathit{\_}\mathit{a}}^2\frac{1}{\sqrt[3]{\mathit{\_}\mathit{C}\mathit{1}+\sqrt{{\mathit{\_}\mathit{a}}^6+{\mathit{\_}\mathit{C}\mathit{1}}^2}}}))}^2)}^{-1}d\mathit{\_}\mathit{a}-x-\mathit{\_}\mathit{C}\mathit{2}=0,{\int }^{y\left(x\right)}{(\frac{{\mathit{\_}\mathit{a}}^2}{2}+\frac{1}{2}{(-\frac{1}{2}\sqrt[3]{\mathit{\_}\mathit{C}\mathit{1}+\sqrt{{\mathit{\_}\mathit{a}}^6+{\mathit{\_}\mathit{C}\mathit{1}}^2}}+\frac{{\mathit{\_}\mathit{a}}^2}{2}\frac{1}{\sqrt[3]{\mathit{\_}\mathit{C}\mathit{1}+\sqrt{{\mathit{\_}\mathit{a}}^6+{\mathit{\_}\mathit{C}\mathit{1}}^2}}}+\frac{i}{2}\sqrt{3}(\sqrt[3]{\mathit{\_}\mathit{C}\mathit{1}+\sqrt{{\mathit{\_}\mathit{a}}^6+{\mathit{\_}\mathit{C}\mathit{1}}^2}}+{\mathit{\_}\mathit{a}}^2\frac{1}{\sqrt[3]{\mathit{\_}\mathit{C}\mathit{1}+\sqrt{{\mathit{\_}\mathit{a}}^6+{\mathit{\_}\mathit{C}\mathit{1}}^2}}}))}^2)}^{-1}d\mathit{\_}\mathit{a}-x-\mathit{\_}\mathit{C}\mathit{2}=0\}$$