8.12   ODE No. 1602

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

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

Mathematica: cpu = 81.621865 (sec), leaf count = 46 $$\text{Solve}[({\int }_1^{y(x)}\frac{1}{\sqrt{c_1-K[1{]}^2(a^{2n}K[1{]}^{2n}-1)}}dK[1]){}^2=(c_2+x){}^2,y(x)]$$

Maple: cpu = 0.125 (sec), leaf count = 73 $$\{{\int }^{y\left(x\right)}\frac{1}{\sqrt{-a^{2n}{\mathit{\_}\mathit{a}}^{2n+2}+{\mathit{\_}\mathit{a}}^2+\mathit{\_}\mathit{C}\mathit{1}}}d\mathit{\_}\mathit{a}-x-\mathit{\_}\mathit{C}\mathit{2}=0,{\int }^{y\left(x\right)}-\frac{1}{\sqrt{-a^{2n}{\mathit{\_}\mathit{a}}^{2n+2}+{\mathit{\_}\mathit{a}}^2+\mathit{\_}\mathit{C}\mathit{1}}}d\mathit{\_}\mathit{a}-x-\mathit{\_}\mathit{C}\mathit{2}=0\}$$