2.1587   ODE No. 1587

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

$$x^5{y}^{(10)}(x)-ay(x)=0$$ ✓ Mathematica : cpu = 0.263024 (sec), leaf count = 492

$$\left\{\{y(x)\to \frac{(-1{)}^{4/5}{a}^{9/5}{c}_1{x}^9{}_0{F}_9(;\frac{6}{5},\frac{7}{5},\frac{8}{5},\frac{9}{5},2,\frac{11}{5},\frac{12}{5},\frac{13}{5},\frac{14}{5};\frac{a{x}^5}{9765625})}{3814697265625}+\frac{(-1{)}^{3/5}{a}^{8/5}{c}_3{x}^8{}_0{F}_9(;\frac{4}{5},\frac{6}{5},\frac{7}{5},\frac{8}{5},\frac{9}{5},2,\frac{11}{5},\frac{12}{5},\frac{13}{5};\frac{a{x}^5}{9765625})}{152587890625}+\frac{(-1{)}^{2/5}{a}^{7/5}{c}_5{x}^7{}_0{F}_9(;\frac{3}{5},\frac{4}{5},\frac{6}{5},\frac{7}{5},\frac{8}{5},\frac{9}{5},2,\frac{11}{5},\frac{12}{5};\frac{a{x}^5}{9765625})}{6103515625}+\frac{\sqrt[5]{-1}{a}^{6/5}{c}_7{x}^6{}_0{F}_9(;\frac{2}{5},\frac{3}{5},\frac{4}{5},\frac{6}{5},\frac{7}{5},\frac{8}{5},\frac{9}{5},2,\frac{11}{5};\frac{a{x}^5}{9765625})}{244140625}+\frac{a{c}_9{x}^5{}_0{F}_9(;\frac{1}{5},\frac{2}{5},\frac{3}{5},\frac{4}{5},\frac{6}{5},\frac{7}{5},\frac{8}{5},\frac{9}{5},2;\frac{a{x}^5}{9765625})}{9765625}+c_{10}{G}_{0,10}^{2,0}\left(\frac{a{x}^5}{9765625}|\begin{array}{c}0,1,\frac{1}{5},\frac{2}{5},\frac{3}{5},\frac{4}{5},\frac{6}{5},\frac{7}{5},\frac{8}{5},\frac{9}{5}\end{array}\right)+c_8{G}_{0,10}^{2,0}\left(\frac{a{x}^5}{9765625}|\begin{array}{c}\frac{1}{5},\frac{6}{5},0,\frac{2}{5},\frac{3}{5},\frac{4}{5},1,\frac{7}{5},\frac{8}{5},\frac{9}{5}\end{array}\right)+c_6{G}_{0,10}^{2,0}\left(\frac{a{x}^5}{9765625}|\begin{array}{c}\frac{2}{5},\frac{7}{5},0,\frac{1}{5},\frac{3}{5},\frac{4}{5},1,\frac{6}{5},\frac{8}{5},\frac{9}{5}\end{array}\right)+c_4{G}_{0,10}^{2,0}\left(\frac{a{x}^5}{9765625}|\begin{array}{c}\frac{3}{5},\frac{8}{5},0,\frac{1}{5},\frac{2}{5},\frac{4}{5},1,\frac{6}{5},\frac{7}{5},\frac{9}{5}\end{array}\right)+c_2{G}_{0,10}^{2,0}\left(\frac{a{x}^5}{9765625}|\begin{array}{c}\frac{4}{5},\frac{9}{5},0,\frac{1}{5},\frac{2}{5},\frac{3}{5},1,\frac{6}{5},\frac{7}{5},\frac{8}{5}\end{array}\right)\}\right\}$$ ✓ Maple : cpu = 0.348 (sec), leaf count = 154

$$\{y\left(x\right)=x^{\frac{5}{2}}(\mathit{\_}\mathit{C}\mathit{10}{\mathit{Y}}_5\left(2{(-1)}^{\frac{9}{10}}{a}^{1/10}\sqrt{x}\right)+\mathit{\_}\mathit{C}\mathit{8}{\mathit{Y}}_5\left(2{(-1)}^{3/10}{a}^{1/10}\sqrt{x}\right)+\mathit{\_}\mathit{C}\mathit{9}{\mathit{Y}}_5\left(2{(-1)}^{\frac{7}{10}}{a}^{1/10}\sqrt{x}\right)+\mathit{\_}\mathit{C}\mathit{7}{\mathit{Y}}_5\left(2{(-1)}^{1/10}{a}^{1/10}\sqrt{x}\right)+\mathit{\_}\mathit{C}\mathit{2}{\mathit{Y}}_5\left(2i{a}^{\frac{1}{10}}\sqrt{x}\right)+\mathit{\_}\mathit{C}\mathit{6}{\mathit{J}}_5\left(2{(-1)}^{\frac{9}{10}}{a}^{1/10}\sqrt{x}\right)+\mathit{\_}\mathit{C}\mathit{5}{\mathit{J}}_5\left(2{(-1)}^{\frac{7}{10}}{a}^{1/10}\sqrt{x}\right)+\mathit{\_}\mathit{C}\mathit{4}{\mathit{J}}_5\left(2{(-1)}^{3/10}{a}^{1/10}\sqrt{x}\right)+\mathit{\_}\mathit{C}\mathit{3}{\mathit{J}}_5\left(2{(-1)}^{1/10}{a}^{1/10}\sqrt{x}\right)+\mathit{\_}\mathit{C}\mathit{1}{\mathit{I}}_5\left(2a^{1/10}\sqrt{x}\right))\}$$