4.151   ODE No. 1151

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

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

Mathematica: cpu = 0.018002 (sec), leaf count = 129 $$\left\{\{y(x)\to \frac{\sqrt{\frac{2}{\pi }}{c}_2\sqrt{x}(i\sinh \left(\sqrt{a}x\right)-\frac{i\cosh \left(\sqrt{a}x\right)}{\sqrt{a}x})}{\sqrt{-i\sqrt{a}x}}+\frac{\sqrt{\frac{2}{\pi }}{c}_1\sqrt{x}(\frac{\sinh \left(\sqrt{a}x\right)}{\sqrt{a}x}-\cosh \left(\sqrt{a}x\right))}{\sqrt{-i\sqrt{a}x}}\}\right\}$$

Maple: cpu = 0.062 (sec), leaf count = 43 $$\{y\left(x\right)=\frac{\mathit{\_}\mathit{C}\mathit{1}}{x}{\mathrm{e}}^{\sqrt{a}x}(-ax+\sqrt{a})+\frac{\mathit{\_}\mathit{C}\mathit{2}}{x}{\mathrm{e}}^{-\sqrt{a}x}(ax+\sqrt{a})\}$$