4.15   ODE No. 1015

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

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

Mathematica: cpu = 0.344544 (sec), leaf count = 26 $$\text{DSolve}[y(x)(1-a^2{x}^{2n})+y^{″}(x)=0,y(x),x]$$

Maple: cpu = 0.156 (sec), leaf count = 31 $$\{y\left(x\right)=\mathit{D}\mathit{E}\mathit{S}\mathit{o}\mathit{l}(\{\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}\mathit{\_}\mathit{Y}\left(x\right)+(-a^2{x}^{2n}+1)\mathit{\_}\mathit{Y}\left(x\right)\},\left\{\mathit{\_}\mathit{Y}\left(x\right)\right\})\}$$