2.1152   ODE No. 1152

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

$$(a^2{x}^2-6)y(x)+x^2{y}^{″}(x)=0$$ ✓ Mathematica : cpu = 0.020343 (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 = 0.228 (sec), leaf count = 67

$$\{y\left(x\right)=\frac{\mathit{\_}\mathit{C}\mathit{1}(\cos \left(ax\right)a^2{x}^2-3\sin \left(ax\right)ax-3\cos \left(ax\right))}{x^2}+\frac{\mathit{\_}\mathit{C}\mathit{2}(\sin \left(ax\right)a^2{x}^2+3\cos \left(ax\right)ax-3\sin \left(ax\right))}{x^2}\}$$