5.48   ODE No. 1496

$$\boxed{{\displaystyle x^2\frac{{\mathrm{d}}^3}{\mathrm{d}{x}^3}y\left(x\right)+6x\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)+6\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+a{x}^{2}y\left(x\right)=0}}$$

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

Mathematica: cpu = 0.273535 (sec), leaf count = 63 $$\left\{\{y(x)\to \frac{c_1{e}^{-\sqrt[3]{a}x}}{x^2}+\frac{c_2{e}^{\sqrt[3]{-1}\sqrt[3]{a}x}}{x^2}+\frac{c_3{e}^{-(-1{)}^{2/3}\sqrt[3]{a}x}}{x^2}\}\right\}$$

Maple: cpu = 0.031 (sec), leaf count = 67 $$\{y\left(x\right)=\frac{1}{x^2}(\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{(-\frac{1}{2}\sqrt[3]{-a}+\frac{i}{2}\sqrt{3}\sqrt[3]{-a})x}+\mathit{\_}\mathit{C}\mathit{2}{\mathrm{e}}^{(-\frac{1}{2}\sqrt[3]{-a}-\frac{i}{2}\sqrt{3}\sqrt[3]{-a})x}+\mathit{\_}\mathit{C}\mathit{3}{\mathrm{e}}^{\sqrt[3]{-a}x})\}$$