8.203   ODE No. 1793

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

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

Mathematica: cpu = 1.371674 (sec), leaf count = 113 $$\left\{\{y(x)\to \text{InverseFunction}[-\frac{a(1-\mathrm{\#}\text{1}{)}^{-1/a}(-(\mathrm{\#}\text{1}-1)\mathrm{\#}\text{1}{)}^{\frac{1}{a}}((a+1){}_2{F}_1(-\frac{1}{a},\frac{1}{a};1+\frac{1}{a};\mathrm{\#}\text{1})+\mathrm{\#}\text{1}{}_2{F}_1(1+\frac{1}{a},\frac{a-1}{a};2+\frac{1}{a};\mathrm{\#}\text{1}))}{a+1}\mathrm{\&}][{\int }_1^x{c}_1{e}^{-{\int }_1^{K[3]}\frac{f(K[1])}{a}dK[1]}dK[3]+c_2]\}\right\}$$

Maple: cpu = 1.747 (sec), leaf count = 40 $$\{\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{-\frac{fx}{a}}-\mathit{\_}\mathit{C}\mathit{2}+{\int }^{y\left(x\right)}\frac{\sqrt[a]{\mathit{\_}\mathit{a}(\mathit{\_}\mathit{a}-1)}}{\mathit{\_}\mathit{a}(\mathit{\_}\mathit{a}-1)}d\mathit{\_}\mathit{a}=0\}$$