8.102   ODE No. 1692

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

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

Mathematica: cpu = 0.083011 (sec), leaf count = 37 $$\text{DSolve}[x^{\frac{n}{n+1}}{y}^{″}(x)-y(x{)}^{\frac{2n+1}{n+1}}=0,y(x),x]$$

Maple: cpu = 3.370 (sec), leaf count = 165 $$\{y\left(x\right)=\mathit{O}\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}\mathit{S}\mathit{t}\mathit{r}\mathit{u}\mathit{c}(\mathit{\_}\mathit{a}{\left({\mathrm{e}}^{\frac{(\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1})(n+2)}{n}}\right)}^{-1},[\{\frac{\mathrm{d}}{\mathrm{d}\mathit{\_}\mathit{a}}\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=-\frac{{\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^3}{n^2}({\mathit{\_}\mathit{a}}^{\frac{2n+1}{n+1}}{n}^2-2\mathit{\_}\mathit{a}{n}^2-6\mathit{\_}\mathit{a}n-4\mathit{\_}\mathit{a})-\frac{(3n+4){\left(\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\right)}^2}{n}\},\{\mathit{\_}\mathit{a}=y\left(x\right)x^{\frac{n+2}{n}},\mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)=\frac{n}{nx\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+ny\left(x\right)+2y\left(x\right)}{\left(x^{\frac{n+2}{n}}\right)}^{-1}\},\{x={\mathrm{e}}^{\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1}},y\left(x\right)=\mathit{\_}\mathit{a}{\left({\mathrm{e}}^{\frac{(\int \mathit{\_}\mathit{b}\left(\mathit{\_}\mathit{a}\right)\mathrm{d}\mathit{\_}\mathit{a}+\mathit{\_}\mathit{C}\mathit{1})(n+2)}{n}}\right)}^{-1}\}])\}$$