5.54   ODE No. 1502

$$\boxed{{\displaystyle x^2\frac{{\mathrm{d}}^3}{\mathrm{d}{x}^3}y\left(x\right)-(x^4-6x)\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)-(2x^3-6)\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)+2x^{2}y\left(x\right)=0}}$$

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

Mathematica: cpu = 0.055007 (sec), leaf count = 98 $$\left\{\{y(x)\to \frac{c_2\mathrm{\Gamma }\left(\frac{1}{3}\right){}_2{F}_2(-\frac{2}{3},\frac{1}{3};\frac{2}{3},\frac{4}{3};\frac{x^3}{3})}{3x\mathrm{\Gamma }\left(\frac{4}{3}\right)}+\frac{\sqrt[3]{-\frac{1}{3}}{c}_3\mathrm{\Gamma }\left(\frac{2}{3}\right){}_2{F}_2(-\frac{1}{3},\frac{2}{3};\frac{4}{3},\frac{5}{3};\frac{x^3}{3})}{3\mathrm{\Gamma }\left(\frac{5}{3}\right)}+\frac{c_1}{x^2}\}\right\}$$

Maple: cpu = 0.328 (sec), leaf count = 109 $$\{y\left(x\right)=\frac{\mathit{\_}\mathit{C}\mathit{1}}{x^2}+\frac{\mathit{\_}\mathit{C}\mathit{2}}{x^2}\int {\mathrm{e}}^{\frac{x^3}{6}}\sqrt{x}({\mathit{I}}_{\frac{1}{6}}(-\frac{x^3}{6})x^3+{\mathit{I}}_{-\frac{5}{6}}(-\frac{x^3}{6})x^3-2{\mathit{I}}_{1/6}(-1/6x^3))\mathrm{d}x+\frac{\mathit{\_}\mathit{C}\mathit{3}}{x^2}\int {\mathrm{e}}^{\frac{x^3}{6}}\sqrt{x}({\mathit{K}}_{\frac{5}{6}}(-\frac{x^3}{6})x^3-{\mathit{K}}_{\frac{1}{6}}(-\frac{x^3}{6})x^3+2{\mathit{K}}_{1/6}(-1/6x^3))\mathrm{d}x\}$$