8.204   ODE No. 1794

$$\boxed{{\displaystyle aby\left(x\right)(-1+y\left(x\right))\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)-((2ab-a-b)y\left(x\right)+(1-a)b){\left(\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)\right)}^2+fy\left(x\right)(-1+y\left(x\right))\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)=0}}$$

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

Mathematica: cpu = 1.296165 (sec), leaf count = 98 $$\left\{\{y(x)\to \text{InverseFunction}[-\frac{a{\mathrm{\#}\text{1}}^{\frac{1}{a}}((a+1){}_2{F}_1(\frac{1}{a},-\frac{1}{b};1+\frac{1}{a};\mathrm{\#}\text{1})+\mathrm{\#}\text{1}{}_2{F}_1(1+\frac{1}{a},\frac{b-1}{b};2+\frac{1}{a};\mathrm{\#}\text{1}))}{a+1}\mathrm{\&}][{\int }_1^x{c}_1{e}^{-{\int }_1^{K[3]}\frac{f(K[1])}{ab}dK[1]}dK[3]+c_2]\}\right\}$$

Maple: cpu = 1.669 (sec), leaf count = 46 $$\{\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{-\frac{fx}{ab}}-\mathit{\_}\mathit{C}\mathit{2}+{\int }^{y\left(x\right)}\frac{\sqrt[a]{\mathit{\_}\mathit{a}}\sqrt[b]{\mathit{\_}\mathit{a}-1}}{\mathit{\_}\mathit{a}(\mathit{\_}\mathit{a}-1)}d\mathit{\_}\mathit{a}=0\}$$