4.272   ODE No. 1272

$$\boxed{{\displaystyle 4x^2\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)+(4a^2{x}^2+1)y\left(x\right)=0}}$$

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

Mathematica: cpu = 0.012002 (sec), leaf count = 32 $$\left\{\{y(x)\to c_1\sqrt{x}{J}_0(ax)+c_2\sqrt{x}{Y}_0(ax)\}\right\}$$

Maple: cpu = 0.031 (sec), leaf count = 25 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}\sqrt{x}{\mathit{J}}_0\left(ax\right)+\mathit{\_}\mathit{C}\mathit{2}\sqrt{x}{\mathit{Y}}_0\left(ax\right)\}$$