4.152   ODE No. 1152

$$\boxed{{\displaystyle x^2\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)+(a^2{x}^2-6)y\left(x\right)=0}}$$

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

Mathematica: cpu = 0.018502 (sec), leaf count = 114 $$\left\{\{y(x)\to \frac{\sqrt{\frac{2}{\pi }}{c}_1\sqrt{x}(\frac{3\sin (ax)}{a^2{x}^2}-\sin (ax)-\frac{3\cos (ax)}{ax})}{\sqrt{ax}}+\frac{\sqrt{\frac{2}{\pi }}{c}_2\sqrt{x}(-\frac{3\cos (ax)}{a^2{x}^2}-\frac{3\sin (ax)}{ax}+\cos (ax))}{\sqrt{ax}}\}\right\}$$

Maple: cpu = 0.171 (sec), leaf count = 67 $$\{y\left(x\right)=\frac{\mathit{\_}\mathit{C}\mathit{1}(\cos \left(ax\right)a^2{x}^2-3\sin \left(ax\right)xa-3\cos \left(ax\right))}{x^2}+\frac{\mathit{\_}\mathit{C}\mathit{2}(\sin \left(ax\right)a^2{x}^2+3\cos \left(ax\right)xa-3\sin \left(ax\right))}{x^2}\}$$