5.76   ODE No. 1524

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

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

Mathematica: cpu = 0.143518 (sec), leaf count = 96 $$\left\{\{y(x)\to -\frac{{(-\frac{1}{3})}^{2/3}{c}_{2}x\mathrm{\Gamma }\left(\frac{1}{3}\right){}_2{F}_2(-\frac{2}{3},\frac{1}{3};\frac{2}{3},\frac{4}{3};\frac{1}{3x^3})}{3\mathrm{\Gamma }\left(\frac{4}{3}\right)}+\frac{c_3\mathrm{\Gamma }\left(\frac{2}{3}\right){}_2{F}_2(-\frac{1}{3},\frac{2}{3};\frac{4}{3},\frac{5}{3};\frac{1}{3x^3})}{9\mathrm{\Gamma }\left(\frac{5}{3}\right)}+c_1{x}^2\}\right\}$$

Maple: cpu = 0.390 (sec), leaf count = 104 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{x}^2+\mathit{\_}\mathit{C}\mathit{2}\int 1{\mathrm{e}}^{\frac{1}{6x^3}}(2x^3{\mathit{I}}_{1/6}(-1/6x^{-3})-{\mathit{I}}_{\frac{1}{6}}(-\frac{1}{6x^3})-{\mathit{I}}_{-\frac{5}{6}}(-\frac{1}{6x^3}))x^{-\frac{11}{2}}\mathrm{d}x{x}^2+\mathit{\_}\mathit{C}\mathit{3}\int 1{\mathrm{e}}^{\frac{1}{6x^3}}(2x^3{\mathit{K}}_{1/6}(-1/6x^{-3})+{\mathit{K}}_{\frac{5}{6}}(-\frac{1}{6x^3})-{\mathit{K}}_{\frac{1}{6}}(-\frac{1}{6x^3}))x^{-\frac{11}{2}}\mathrm{d}x{x}^2\}$$