3.518   ODE No. 518

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

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

Mathematica: cpu = 0.801102 (sec), leaf count = 236 $$\{\{y(x)\to \text{InverseFunction}[-\frac{3\sqrt[3]{a-\mathrm{\#}\text{1}}{\left(\frac{\mathrm{\#}\text{1}-b}{a-b}\right)}^{2/3}{}_2{F}_1(\frac{1}{3},\frac{2}{3};\frac{4}{3};\frac{a-\mathrm{\#}\text{1}}{a-b})}{(b-\mathrm{\#}\text{1}{)}^{2/3}}\mathrm{\&}][c_1+x]\},\{y(x)\to \text{InverseFunction}[-\frac{3\sqrt[3]{a-\mathrm{\#}\text{1}}{\left(\frac{\mathrm{\#}\text{1}-b}{a-b}\right)}^{2/3}{}_2{F}_1(\frac{1}{3},\frac{2}{3};\frac{4}{3};\frac{a-\mathrm{\#}\text{1}}{a-b})}{(b-\mathrm{\#}\text{1}{)}^{2/3}}\mathrm{\&}][c_1-\sqrt[3]{-1}x]\},\{y(x)\to \text{InverseFunction}[-\frac{3\sqrt[3]{a-\mathrm{\#}\text{1}}{\left(\frac{\mathrm{\#}\text{1}-b}{a-b}\right)}^{2/3}{}_2{F}_1(\frac{1}{3},\frac{2}{3};\frac{4}{3};\frac{a-\mathrm{\#}\text{1}}{a-b})}{(b-\mathrm{\#}\text{1}{)}^{2/3}}\mathrm{\&}][c_1+(-1{)}^{2/3}x]\}\}$$

Maple: cpu = 0.156 (sec), leaf count = 126 $$\{x-{\int }^{y\left(x\right)}\frac{1}{\sqrt[3]{{(\mathit{\_}\mathit{a}-a)}^2{(-b+\mathit{\_}\mathit{a})}^2}}d\mathit{\_}\mathit{a}-\mathit{\_}\mathit{C}\mathit{1}=0,x-{\int }^{y\left(x\right)}2\frac{1}{(i\sqrt{3}-1)\sqrt[3]{{(\mathit{\_}\mathit{a}-a)}^2{(-b+\mathit{\_}\mathit{a})}^2}}d\mathit{\_}\mathit{a}-\mathit{\_}\mathit{C}\mathit{1}=0,x-{\int }^{y\left(x\right)}-2\frac{1}{(i\sqrt{3}+1)\sqrt[3]{{(\mathit{\_}\mathit{a}-a)}^2{(-b+\mathit{\_}\mathit{a})}^2}}d\mathit{\_}\mathit{a}-\mathit{\_}\mathit{C}\mathit{1}=0,y\left(x\right)=a,y\left(x\right)=b\}$$