4.150   ODE No. 1150

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

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

Mathematica: cpu = 0.009001 (sec), leaf count = 53 $$\left\{\{y(x)\to \sqrt{\frac{2}{\pi }}{c}_2(-\sin (x)-\frac{\cos (x)}{x})+\sqrt{\frac{2}{\pi }}{c}_1(\frac{\sin (x)}{x}-\cos (x))\}\right\}$$

Maple: cpu = 0.063 (sec), leaf count = 31 $$\{y\left(x\right)=\frac{\mathit{\_}\mathit{C}\mathit{1}(\cos \left(x\right)x-\sin \left(x\right))}{x}+\frac{\mathit{\_}\mathit{C}\mathit{2}(\cos \left(x\right)+x\sin \left(x\right))}{x}\}$$