2.518   ODE No. 518

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

$$y^{\prime }(x{)}^3-(y(x)-a{)}^2(y(x)-b{)}^2=0$$ ✓ Mathematica : cpu = 0.510286 (sec), leaf count = 236

$$\{\{y(x)\to \text{InverseFunction}[-\frac{3\sqrt[3]{a-\mathrm{\#}\text{1}}{\left(\frac{\mathrm{\#}\text{1}-b}{a-b}\right)}^{2/3}{}_2{F}_1(\frac{1}{3},\frac{2}{3};\frac{4}{3};\frac{a-\mathrm{\#}\text{1}}{a-b})}{(b-\mathrm{\#}\text{1}{)}^{2/3}}\mathrm{\&}][x+c_1]\},\{y(x)\to \text{InverseFunction}[-\frac{3\sqrt[3]{a-\mathrm{\#}\text{1}}{\left(\frac{\mathrm{\#}\text{1}-b}{a-b}\right)}^{2/3}{}_2{F}_1(\frac{1}{3},\frac{2}{3};\frac{4}{3};\frac{a-\mathrm{\#}\text{1}}{a-b})}{(b-\mathrm{\#}\text{1}{)}^{2/3}}\mathrm{\&}][-\sqrt[3]{-1}x+c_1]\},\{y(x)\to \text{InverseFunction}[-\frac{3\sqrt[3]{a-\mathrm{\#}\text{1}}{\left(\frac{\mathrm{\#}\text{1}-b}{a-b}\right)}^{2/3}{}_2{F}_1(\frac{1}{3},\frac{2}{3};\frac{4}{3};\frac{a-\mathrm{\#}\text{1}}{a-b})}{(b-\mathrm{\#}\text{1}{)}^{2/3}}\mathrm{\&}][(-1{)}^{2/3}x+c_1]\}\}$$ ✓ Maple : cpu = 0.786 (sec), leaf count = 126

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