3.530   ODE No. 530

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

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

Mathematica: cpu = 0 (sec), leaf count = 0 $$\text{Hanged}$$

Maple: cpu = 0.094 (sec), leaf count = 421 $$\{x-{\int }^{y\left(x\right)}6\frac{\sqrt[3]{-108{\mathit{\_}\mathit{a}}^2+8{\mathit{\_}\mathit{a}}^3+12\sqrt{-3{\mathit{\_}\mathit{a}}^4(4\mathit{\_}\mathit{a}-27)}}}{4{\mathit{\_}\mathit{a}}^2+2\mathit{\_}\mathit{a}\sqrt[3]{-108{\mathit{\_}\mathit{a}}^2+8{\mathit{\_}\mathit{a}}^3+12\sqrt{-3{\mathit{\_}\mathit{a}}^4(4\mathit{\_}\mathit{a}-27)}}+{(-108{\mathit{\_}\mathit{a}}^2+8{\mathit{\_}\mathit{a}}^3+12\sqrt{-3{\mathit{\_}\mathit{a}}^4(4\mathit{\_}\mathit{a}-27)})}^{2/3}}d\mathit{\_}\mathit{a}-\mathit{\_}\mathit{C}\mathit{1}=0,x-{\int }^{y\left(x\right)}24\frac{\sqrt[3]{-108{\mathit{\_}\mathit{a}}^2+8{\mathit{\_}\mathit{a}}^3+12\sqrt{-3{\mathit{\_}\mathit{a}}^4(4\mathit{\_}\mathit{a}-27)}}}{(i\sqrt{3}-1)(2\mathit{\_}\mathit{a}-\sqrt[3]{-108{\mathit{\_}\mathit{a}}^2+8{\mathit{\_}\mathit{a}}^3+12\sqrt{-3{\mathit{\_}\mathit{a}}^4(4\mathit{\_}\mathit{a}-27)}})(-i\sqrt{3}\sqrt[3]{-108{\mathit{\_}\mathit{a}}^2+8{\mathit{\_}\mathit{a}}^3+12\sqrt{-3{\mathit{\_}\mathit{a}}^4(4\mathit{\_}\mathit{a}-27)}}+4\mathit{\_}\mathit{a}+\sqrt[3]{-108{\mathit{\_}\mathit{a}}^2+8{\mathit{\_}\mathit{a}}^3+12\sqrt{-3{\mathit{\_}\mathit{a}}^4(4\mathit{\_}\mathit{a}-27)}})}d\mathit{\_}\mathit{a}-\mathit{\_}\mathit{C}\mathit{1}=0,x-{\int }^{y\left(x\right)}-24\frac{\sqrt[3]{-108{\mathit{\_}\mathit{a}}^2+8{\mathit{\_}\mathit{a}}^3+12\sqrt{-3{\mathit{\_}\mathit{a}}^4(4\mathit{\_}\mathit{a}-27)}}}{(i\sqrt{3}+1)(2\mathit{\_}\mathit{a}-\sqrt[3]{-108{\mathit{\_}\mathit{a}}^2+8{\mathit{\_}\mathit{a}}^3+12\sqrt{-3{\mathit{\_}\mathit{a}}^4(4\mathit{\_}\mathit{a}-27)}})(i\sqrt{3}\sqrt[3]{-108{\mathit{\_}\mathit{a}}^2+8{\mathit{\_}\mathit{a}}^3+12\sqrt{-3{\mathit{\_}\mathit{a}}^4(4\mathit{\_}\mathit{a}-27)}}+4\mathit{\_}\mathit{a}+\sqrt[3]{-108{\mathit{\_}\mathit{a}}^2+8{\mathit{\_}\mathit{a}}^3+12\sqrt{-3{\mathit{\_}\mathit{a}}^4(4\mathit{\_}\mathit{a}-27)}})}d\mathit{\_}\mathit{a}-\mathit{\_}\mathit{C}\mathit{1}=0,y\left(x\right)=0\}$$