3.548   ODE No. 548

$$\boxed{{\displaystyle {\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^6-{(y\left(x\right)-a)}^4{(y\left(x\right)-b)}^3=0}}$$

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

Mathematica: cpu = 1.005628 (sec), leaf count = 569 $$\{\{y(x)\to \text{InverseFunction}[-\frac{\sqrt[3]{a-\mathrm{\#}\text{1}}\sqrt{\frac{\mathrm{\#}\text{1}-b}{a-b}}{B}_{\frac{a-\mathrm{\#}\text{1}}{a-b}}(\frac{1}{3},\frac{1}{2})}{\sqrt{b-\mathrm{\#}\text{1}}\sqrt[3]{\frac{a-\mathrm{\#}\text{1}}{a-b}}}\mathrm{\&}][c_1-ix]\},\{y(x)\to \text{InverseFunction}[-\frac{\sqrt[3]{a-\mathrm{\#}\text{1}}\sqrt{\frac{\mathrm{\#}\text{1}-b}{a-b}}{B}_{\frac{a-\mathrm{\#}\text{1}}{a-b}}(\frac{1}{3},\frac{1}{2})}{\sqrt{b-\mathrm{\#}\text{1}}\sqrt[3]{\frac{a-\mathrm{\#}\text{1}}{a-b}}}\mathrm{\&}][c_1+ix]\},\{y(x)\to \text{InverseFunction}[-\frac{\sqrt[3]{a-\mathrm{\#}\text{1}}\sqrt{\frac{\mathrm{\#}\text{1}-b}{a-b}}{B}_{\frac{a-\mathrm{\#}\text{1}}{a-b}}(\frac{1}{3},\frac{1}{2})}{\sqrt{b-\mathrm{\#}\text{1}}\sqrt[3]{\frac{a-\mathrm{\#}\text{1}}{a-b}}}\mathrm{\&}][c_1-\sqrt[6]{-1}x]\},\{y(x)\to \text{InverseFunction}[-\frac{\sqrt[3]{a-\mathrm{\#}\text{1}}\sqrt{\frac{\mathrm{\#}\text{1}-b}{a-b}}{B}_{\frac{a-\mathrm{\#}\text{1}}{a-b}}(\frac{1}{3},\frac{1}{2})}{\sqrt{b-\mathrm{\#}\text{1}}\sqrt[3]{\frac{a-\mathrm{\#}\text{1}}{a-b}}}\mathrm{\&}][c_1+\sqrt[6]{-1}x]\},\{y(x)\to \text{InverseFunction}[-\frac{\sqrt[3]{a-\mathrm{\#}\text{1}}\sqrt{\frac{\mathrm{\#}\text{1}-b}{a-b}}{B}_{\frac{a-\mathrm{\#}\text{1}}{a-b}}(\frac{1}{3},\frac{1}{2})}{\sqrt{b-\mathrm{\#}\text{1}}\sqrt[3]{\frac{a-\mathrm{\#}\text{1}}{a-b}}}\mathrm{\&}][c_1-(-1{)}^{5/6}x]\},\{y(x)\to \text{InverseFunction}[-\frac{\sqrt[3]{a-\mathrm{\#}\text{1}}\sqrt{\frac{\mathrm{\#}\text{1}-b}{a-b}}{B}_{\frac{a-\mathrm{\#}\text{1}}{a-b}}(\frac{1}{3},\frac{1}{2})}{\sqrt{b-\mathrm{\#}\text{1}}\sqrt[3]{\frac{a-\mathrm{\#}\text{1}}{a-b}}}\mathrm{\&}][c_1+(-1{)}^{5/6}x]\}\}$$

Maple: cpu = 0.234 (sec), leaf count = 241 $$\{x-{\int }^{y\left(x\right)}\frac{1}{\sqrt[6]{{(\mathit{\_}\mathit{a}-a)}^4{(-b+\mathit{\_}\mathit{a})}^3}}d\mathit{\_}\mathit{a}-\mathit{\_}\mathit{C}\mathit{1}=0,x-{\int }^{y\left(x\right)}\frac{-2i}{\sqrt{3}-i}\frac{1}{\sqrt[6]{{(\mathit{\_}\mathit{a}-a)}^4{(-b+\mathit{\_}\mathit{a})}^3}}d\mathit{\_}\mathit{a}-\mathit{\_}\mathit{C}\mathit{1}=0,x-{\int }^{y\left(x\right)}\frac{-2i}{\sqrt{3}+i}\frac{1}{\sqrt[6]{{(\mathit{\_}\mathit{a}-a)}^4{(-b+\mathit{\_}\mathit{a})}^3}}d\mathit{\_}\mathit{a}-\mathit{\_}\mathit{C}\mathit{1}=0,x-{\int }^{y\left(x\right)}\frac{2i}{\sqrt{3}-i}\frac{1}{\sqrt[6]{{(\mathit{\_}\mathit{a}-a)}^4{(-b+\mathit{\_}\mathit{a})}^3}}d\mathit{\_}\mathit{a}-\mathit{\_}\mathit{C}\mathit{1}=0,x-{\int }^{y\left(x\right)}\frac{2i}{\sqrt{3}+i}\frac{1}{\sqrt[6]{{(\mathit{\_}\mathit{a}-a)}^4{(-b+\mathit{\_}\mathit{a})}^3}}d\mathit{\_}\mathit{a}-\mathit{\_}\mathit{C}\mathit{1}=0,x-{\int }^{y\left(x\right)}-\frac{1}{\sqrt[6]{{(\mathit{\_}\mathit{a}-a)}^4{(-b+\mathit{\_}\mathit{a})}^3}}d\mathit{\_}\mathit{a}-\mathit{\_}\mathit{C}\mathit{1}=0,y\left(x\right)=a,y\left(x\right)=b\}$$