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 = 0.690435 (sec), leaf count = 323

$$\{\{y(x)\to \text{InverseFunction}[-\frac{4\sqrt[4]{a-\mathrm{\#}\text{1}}\sqrt{\frac{\mathrm{\#}\text{1}-b}{a-b}}{}_2{F}_1(\frac{1}{4},\frac{1}{2};\frac{5}{4};\frac{a-\mathrm{\#}\text{1}}{a-b})}{\sqrt{b-\mathrm{\#}\text{1}}}\mathrm{\&}][-\sqrt[4]{-1}x+c_1]\},\{y(x)\to \text{InverseFunction}[-\frac{4\sqrt[4]{a-\mathrm{\#}\text{1}}\sqrt{\frac{\mathrm{\#}\text{1}-b}{a-b}}{}_2{F}_1(\frac{1}{4},\frac{1}{2};\frac{5}{4};\frac{a-\mathrm{\#}\text{1}}{a-b})}{\sqrt{b-\mathrm{\#}\text{1}}}\mathrm{\&}][\sqrt[4]{-1}x+c_1]\},\{y(x)\to \text{InverseFunction}[-\frac{4\sqrt[4]{a-\mathrm{\#}\text{1}}\sqrt{\frac{\mathrm{\#}\text{1}-b}{a-b}}{}_2{F}_1(\frac{1}{4},\frac{1}{2};\frac{5}{4};\frac{a-\mathrm{\#}\text{1}}{a-b})}{\sqrt{b-\mathrm{\#}\text{1}}}\mathrm{\&}][-(-1{)}^{3/4}x+c_1]\},\{y(x)\to \text{InverseFunction}[-\frac{4\sqrt[4]{a-\mathrm{\#}\text{1}}\sqrt{\frac{\mathrm{\#}\text{1}-b}{a-b}}{}_2{F}_1(\frac{1}{4},\frac{1}{2};\frac{5}{4};\frac{a-\mathrm{\#}\text{1}}{a-b})}{\sqrt{b-\mathrm{\#}\text{1}}}\mathrm{\&}][(-1{)}^{3/4}x+c_1]\}\}$$ ✓ Maple : cpu = 0.23 (sec), leaf count = 144

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