4.213   ODE No. 1213

$$\boxed{{\displaystyle x^2\frac{{\mathrm{d}}^2}{\mathrm{d}{x}^2}y\left(x\right)+(x^3+1)x\frac{\mathrm{d}}{\mathrm{d}x}y\left(x\right)-y\left(x\right)=0}}$$

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

Mathematica: cpu = 0.072009 (sec), leaf count = 54 $$\left\{\{y(x)\to \frac{\sqrt[3]{3}{c}_1{}_1{F}_1(-\frac{1}{3};\frac{1}{3};-\frac{x^3}{3})}{x}+\frac{c_{2}x{}_1{F}_1(\frac{1}{3};\frac{5}{3};-\frac{x^3}{3})}{\sqrt[3]{3}}\}\right\}$$

Maple: cpu = 0.047 (sec), leaf count = 59 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^{-\frac{x^3}{6}}{x}^{\frac{3}{2}}({\mathit{I}}_{\frac{5}{6}}\left(\frac{x^3}{6}\right)+{\mathit{I}}_{-\frac{1}{6}}\left(\frac{x^3}{6}\right))+\mathit{\_}\mathit{C}\mathit{2}{\mathrm{e}}^{-\frac{x^3}{6}}{x}^{\frac{3}{2}}({\mathit{K}}_{\frac{1}{6}}\left(\frac{x^3}{6}\right)-{\mathit{K}}_{\frac{5}{6}}\left(\frac{x^3}{6}\right))\}$$