4.59   ODE No. 1059

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

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

Mathematica: cpu = 0.052007 (sec), leaf count = 72 $$\left\{\{y(x)\to c_{1}x-\frac{c_2{e}^{-\frac{x^5}{5}}(5{\left(x^5\right)}^{4/5}-5^{4/5}{e}^{\frac{x^5}{5}}{x}^5\mathrm{\Gamma }(\frac{4}{5},\frac{x^5}{5}))}{5{\left(x^5\right)}^{4/5}}\}\right\}$$

Maple: cpu = 0.062 (sec), leaf count = 55 $$\{y\left(x\right)=x\mathit{\_}\mathit{C}\mathit{1}+\frac{\mathit{\_}\mathit{C}\mathit{2}}{x^7}{\mathrm{e}}^{-\frac{x^5}{10}}(x^{10}{\mathit{M}}_{\frac{2}{5},\frac{9}{10}}\left(\frac{x^5}{5}\right)+9{\mathit{M}}_{7/5,\frac{9}{10}}\left(1/5x^5\right)x^5+36{\mathit{M}}_{7/5,\frac{9}{10}}\left(1/5x^5\right))\}$$