2.545   ODE No. 545

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

$$y^{\prime }(x{)}^4-(y(x)-a{)}^3(y(x)-b{)}^2=0$$ ✓ Mathematica : cpu = 0.716669 (sec), leaf count = 383

$$\{\{y(x)\to \text{InverseFunction}[-\frac{\sqrt[4]{a-\mathrm{\#}\text{1}}\sqrt{\frac{\mathrm{\#}\text{1}-b}{a-b}}{B}_{\frac{a-\mathrm{\#}\text{1}}{a-b}}(\frac{1}{4},\frac{1}{2})}{\sqrt{b-\mathrm{\#}\text{1}}\sqrt[4]{\frac{a-\mathrm{\#}\text{1}}{a-b}}}\mathrm{\&}][c_1-\sqrt[4]{-1}x]\},\{y(x)\to \text{InverseFunction}[-\frac{\sqrt[4]{a-\mathrm{\#}\text{1}}\sqrt{\frac{\mathrm{\#}\text{1}-b}{a-b}}{B}_{\frac{a-\mathrm{\#}\text{1}}{a-b}}(\frac{1}{4},\frac{1}{2})}{\sqrt{b-\mathrm{\#}\text{1}}\sqrt[4]{\frac{a-\mathrm{\#}\text{1}}{a-b}}}\mathrm{\&}][c_1+\sqrt[4]{-1}x]\},\{y(x)\to \text{InverseFunction}[-\frac{\sqrt[4]{a-\mathrm{\#}\text{1}}\sqrt{\frac{\mathrm{\#}\text{1}-b}{a-b}}{B}_{\frac{a-\mathrm{\#}\text{1}}{a-b}}(\frac{1}{4},\frac{1}{2})}{\sqrt{b-\mathrm{\#}\text{1}}\sqrt[4]{\frac{a-\mathrm{\#}\text{1}}{a-b}}}\mathrm{\&}][c_1-(-1{)}^{3/4}x]\},\{y(x)\to \text{InverseFunction}[-\frac{\sqrt[4]{a-\mathrm{\#}\text{1}}\sqrt{\frac{\mathrm{\#}\text{1}-b}{a-b}}{B}_{\frac{a-\mathrm{\#}\text{1}}{a-b}}(\frac{1}{4},\frac{1}{2})}{\sqrt{b-\mathrm{\#}\text{1}}\sqrt[4]{\frac{a-\mathrm{\#}\text{1}}{a-b}}}\mathrm{\&}][c_1+(-1{)}^{3/4}x]\}\}$$

✓ Maple : cpu = 0.345 (sec), leaf count = 141

$$\{x-{\int }^{y\left(x\right)}\frac{1}{\sqrt[4]{{(\mathit{\_}\mathit{a}-a)}^3{(\mathit{\_}\mathit{a}-b)}^2}}d\mathit{\_}\mathit{a}-\mathit{\_}\mathit{C}\mathit{1}=0,x-{\int }^{y\left(x\right)}-i\frac{1}{\sqrt[4]{{(\mathit{\_}\mathit{a}-a)}^3{(\mathit{\_}\mathit{a}-b)}^2}}d\mathit{\_}\mathit{a}-\mathit{\_}\mathit{C}\mathit{1}=0,x-{\int }^{y\left(x\right)}i\frac{1}{\sqrt[4]{{(\mathit{\_}\mathit{a}-a)}^3{(\mathit{\_}\mathit{a}-b)}^2}}d\mathit{\_}\mathit{a}-\mathit{\_}\mathit{C}\mathit{1}=0,x-{\int }^{y\left(x\right)}-\frac{1}{\sqrt[4]{{(\mathit{\_}\mathit{a}-a)}^3{(\mathit{\_}\mathit{a}-b)}^2}}d\mathit{\_}\mathit{a}-\mathit{\_}\mathit{C}\mathit{1}=0,y\left(x\right)=a,y\left(x\right)=b\}$$