4.299   ODE No. 1299

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

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

Mathematica: cpu = 0.014002 (sec), leaf count = 19 $$\left\{\{y(x)\to c_2-\frac{c_1{\tanh }^{-1}(ax)}{a}\}\right\}$$

Maple: cpu = 0.016 (sec), leaf count = 31 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}+(\frac{\ln (ax-1)}{2a}-\frac{\ln (ax+1)}{2a})\mathit{\_}\mathit{C}\mathit{2}\}$$