2.530   ODE No. 530

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

$$y^{\prime }(x{)}^3-y(x)y^{\prime }(x{)}^2+y(x{)}^2=0$$ ✓ Mathematica : cpu = 7.97625 (sec), leaf count = 648

$$\{\{y(x)\to \text{InverseFunction}[{\int }_1^{\mathrm{\#}\text{1}}\frac{\sqrt[3]{2K[1{]}^3-27K[1{]}^2+3\sqrt{3}\sqrt{-K[1{]}^4(4K[1]-27)}}}{2\sqrt[3]{2}K[1{]}^2+2\sqrt[3]{2K[1{]}^3-27K[1{]}^2+3\sqrt{3}\sqrt{-K[1{]}^4(4K[1]-27)}}K[1]+2^{2/3}{(2K[1{]}^3-27K[1{]}^2+3\sqrt{3}\sqrt{-K[1{]}^4(4K[1]-27)})}^{2/3}}dK[1]\mathrm{\&}][c_1+\frac{x}{6}]\},\{y(x)\to \text{InverseFunction}[{\int }_1^{\mathrm{\#}\text{1}}\frac{\sqrt[3]{2K[2{]}^3-27K[2{]}^2+3\sqrt{3}\sqrt{-K[2{]}^4(4K[2]-27)}}}{2i\sqrt[3]{2}\sqrt{3}K[2{]}^2-2\sqrt[3]{2}K[2{]}^2+4\sqrt[3]{2K[2{]}^3-27K[2{]}^2+3\sqrt{3}\sqrt{-K[2{]}^4(4K[2]-27)}}K[2]-i{2}^{2/3}\sqrt{3}{(2K[2{]}^3-27K[2{]}^2+3\sqrt{3}\sqrt{-K[2{]}^4(4K[2]-27)})}^{2/3}-2^{2/3}{(2K[2{]}^3-27K[2{]}^2+3\sqrt{3}\sqrt{-K[2{]}^4(4K[2]-27)})}^{2/3}}dK[2]\mathrm{\&}][c_1+\frac{x}{12}]\},\{y(x)\to \text{InverseFunction}[{\int }_1^{\mathrm{\#}\text{1}}\frac{\sqrt[3]{2K[3{]}^3-27K[3{]}^2+3\sqrt{3}\sqrt{-K[3{]}^4(4K[3]-27)}}}{-2i\sqrt[3]{2}\sqrt{3}K[3{]}^2-2\sqrt[3]{2}K[3{]}^2+4\sqrt[3]{2K[3{]}^3-27K[3{]}^2+3\sqrt{3}\sqrt{-K[3{]}^4(4K[3]-27)}}K[3]+i{2}^{2/3}\sqrt{3}{(2K[3{]}^3-27K[3{]}^2+3\sqrt{3}\sqrt{-K[3{]}^4(4K[3]-27)})}^{2/3}-2^{2/3}{(2K[3{]}^3-27K[3{]}^2+3\sqrt{3}\sqrt{-K[3{]}^4(4K[3]-27)})}^{2/3}}dK[3]\mathrm{\&}][c_1+\frac{x}{12}]\}\}$$ ✓ Maple : cpu = 0.086 (sec), leaf count = 432

$$\{x-{\int }^{y\left(x\right)}6\frac{\sqrt[3]{-108{\mathit{\_}\mathit{a}}^2+8{\mathit{\_}\mathit{a}}^3+12\sqrt{-12{\mathit{\_}\mathit{a}}^5+81{\mathit{\_}\mathit{a}}^4}}}{4{\mathit{\_}\mathit{a}}^2+2\mathit{\_}\mathit{a}\sqrt[3]{-108{\mathit{\_}\mathit{a}}^2+8{\mathit{\_}\mathit{a}}^3+12\sqrt{-12{\mathit{\_}\mathit{a}}^5+81{\mathit{\_}\mathit{a}}^4}}+{(-108{\mathit{\_}\mathit{a}}^2+8{\mathit{\_}\mathit{a}}^3+12\sqrt{-12{\mathit{\_}\mathit{a}}^5+81{\mathit{\_}\mathit{a}}^4})}^{2/3}}d\mathit{\_}\mathit{a}-\mathit{\_}\mathit{C}\mathit{1}=0,x-{\int }^{y\left(x\right)}-24\frac{\sqrt[3]{-108{\mathit{\_}\mathit{a}}^2+8{\mathit{\_}\mathit{a}}^3+12\sqrt{-12{\mathit{\_}\mathit{a}}^5+81{\mathit{\_}\mathit{a}}^4}}}{(i\sqrt{3}-1)(i\sqrt{3}\sqrt[3]{-108{\mathit{\_}\mathit{a}}^2+8{\mathit{\_}\mathit{a}}^3+12\sqrt{-12{\mathit{\_}\mathit{a}}^5+81{\mathit{\_}\mathit{a}}^4}}-\sqrt[3]{-108{\mathit{\_}\mathit{a}}^2+8{\mathit{\_}\mathit{a}}^3+12\sqrt{-12{\mathit{\_}\mathit{a}}^5+81{\mathit{\_}\mathit{a}}^4}}-4\mathit{\_}\mathit{a})(2\mathit{\_}\mathit{a}-\sqrt[3]{-108{\mathit{\_}\mathit{a}}^2+8{\mathit{\_}\mathit{a}}^3+12\sqrt{-12{\mathit{\_}\mathit{a}}^5+81{\mathit{\_}\mathit{a}}^4}})}d\mathit{\_}\mathit{a}-\mathit{\_}\mathit{C}\mathit{1}=0,x-{\int }^{y\left(x\right)}24\frac{\sqrt[3]{-108{\mathit{\_}\mathit{a}}^2+8{\mathit{\_}\mathit{a}}^3+12\sqrt{-12{\mathit{\_}\mathit{a}}^5+81{\mathit{\_}\mathit{a}}^4}}}{(i\sqrt{3}+1)(-2\mathit{\_}\mathit{a}+\sqrt[3]{-108{\mathit{\_}\mathit{a}}^2+8{\mathit{\_}\mathit{a}}^3+12\sqrt{-12{\mathit{\_}\mathit{a}}^5+81{\mathit{\_}\mathit{a}}^4}})(i\sqrt{3}\sqrt[3]{-108{\mathit{\_}\mathit{a}}^2+8{\mathit{\_}\mathit{a}}^3+12\sqrt{-12{\mathit{\_}\mathit{a}}^5+81{\mathit{\_}\mathit{a}}^4}}+4\mathit{\_}\mathit{a}+\sqrt[3]{-108{\mathit{\_}\mathit{a}}^2+8{\mathit{\_}\mathit{a}}^3+12\sqrt{-12{\mathit{\_}\mathit{a}}^5+81{\mathit{\_}\mathit{a}}^4}})}d\mathit{\_}\mathit{a}-\mathit{\_}\mathit{C}\mathit{1}=0,y\left(x\right)=0\}$$