8.57   ODE No. 1647

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

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

Mathematica: cpu = 48.122611 (sec), leaf count = 59 $$\left\{\{y(x)\to x({\int }_1^x(\frac{1}{2}aK[2{]}^{2r}-\frac{1}{2}arK[2{]}^{2r}+c_{1}K[2{]}^{2r-2}){}^{\frac{1}{1-r}}dK[2]+c_2)\}\right\}$$

Maple: cpu = 0.312 (sec), leaf count = 123 $$\{y\left(x\right)=(\int -\frac{ar}{2}{2}^{\frac{r}{r-1}}{\left({(-ar{x}^2+a{x}^2+\mathit{\_}\mathit{C}\mathit{1})}^{-1}\right)}^{\frac{r}{r-1}}+\frac{a}{2}{2}^{\frac{r}{r-1}}{\left({(-ar{x}^2+a{x}^2+\mathit{\_}\mathit{C}\mathit{1})}^{-1}\right)}^{\frac{r}{r-1}}+\frac{\mathit{\_}\mathit{C}\mathit{1}}{2x^2}{2}^{\frac{r}{r-1}}{\left({(-ar{x}^2+a{x}^2+\mathit{\_}\mathit{C}\mathit{1})}^{-1}\right)}^{\frac{r}{r-1}}\mathrm{d}x+\mathit{\_}\mathit{C}\mathit{2})x\}$$