2.1151   ODE No. 1151

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

$$x^2{y}^{″}(x)-(a{x}^2+2)y(x)=0$$ ✓ Mathematica : cpu = 0.0117585 (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 = 0.192 (sec), leaf count = 43

$$\{y\left(x\right)=\frac{1}{x}(\mathit{\_}\mathit{C}\mathit{2}(ax+\sqrt{a}){\mathrm{e}}^{-\sqrt{a}x}-\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{\sqrt{a}x}(ax-\sqrt{a}))\}$$