7.11   ODE No. 1584

$$\boxed{{\displaystyle x\frac{{\mathrm{d}}^5}{\mathrm{d}{x}^5}y\left(x\right)-5m\frac{{\mathrm{d}}^4}{\mathrm{d}{x}^4}y\left(x\right)+axy\left(x\right)=0}}$$

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

Mathematica: cpu = 2.837860 (sec), leaf count = 216 $$\left\{\{y(x)\to c_5{5}^{-5m-4}{a}^{\frac{1}{5}(5m+4)}{x}^{5m+4}{}_0{F}_4(;m+\frac{6}{5},m+\frac{7}{5},m+\frac{8}{5},m+\frac{9}{5};-\frac{a{x}^5}{3125})+\frac{1}{125}{a}^{3/5}{c}_4{x}^3{}_0{F}_4(;\frac{6}{5},\frac{7}{5},\frac{8}{5},\frac{4}{5}-m;-\frac{a{x}^5}{3125})+\frac{1}{25}{a}^{2/5}{c}_3{x}^2{}_0{F}_4(;\frac{4}{5},\frac{6}{5},\frac{7}{5},\frac{3}{5}-m;-\frac{a{x}^5}{3125})+\frac{1}{5}\sqrt[5]{a}{c}_{2}x{}_0{F}_4(;\frac{3}{5},\frac{4}{5},\frac{6}{5},\frac{2}{5}-m;-\frac{a{x}^5}{3125})+c_1{}_0{F}_4(;\frac{2}{5},\frac{3}{5},\frac{4}{5},\frac{1}{5}-m;-\frac{a{x}^5}{3125})\}\right\}$$

Maple: cpu = 0.124 (sec), leaf count = 118 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{}_0\text{F}{}_4(;\frac{2}{5},\frac{3}{5},\frac{4}{5},\frac{1}{5}-m;-\frac{x^{5}a}{3125})+\mathit{\_}\mathit{C}\mathit{2}x{}_0\text{F}{}_4(;\frac{3}{5},\frac{4}{5},\frac{6}{5},\frac{2}{5}-m;-\frac{x^{5}a}{3125})+\mathit{\_}\mathit{C}\mathit{3}{x}^2{}_0\text{F}{}_4(;\frac{4}{5},\frac{6}{5},\frac{7}{5},\frac{3}{5}-m;-\frac{x^{5}a}{3125})+\mathit{\_}\mathit{C}\mathit{4}{x}^3{}_0\text{F}{}_4(;\frac{6}{5},\frac{7}{5},\frac{8}{5},\frac{4}{5}-m;-\frac{x^{5}a}{3125})+\mathit{\_}\mathit{C}\mathit{5}{x}^{4+5m}{}_0\text{F}{}_4(;\frac{9}{5}+m,\frac{8}{5}+m,\frac{7}{5}+m,\frac{6}{5}+m;-\frac{x^{5}a}{3125})\}$$