7.14   ODE No. 1587

$$\boxed{{\displaystyle x^5\frac{{\mathrm{d}}^{10}}{\mathrm{d}{x}^{10}}y\left(x\right)-ay\left(x\right)=0}}$$

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

Mathematica: cpu = 0.311540 (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 = 0.265 (sec), leaf count = 200 $$\{y\left(x\right)=\mathit{\_}\mathit{C}\mathit{1}{x}^{\frac{5}{2}}{\mathit{I}}_5\left(2a^{1/10}\sqrt{x}\right)+\mathit{\_}\mathit{C}\mathit{2}{x}^{\frac{5}{2}}{\mathit{Y}}_5\left(2i{a}^{\frac{1}{10}}\sqrt{x}\right)+\mathit{\_}\mathit{C}\mathit{3}{x}^{\frac{5}{2}}{\mathit{I}}_5\left(2{\mathrm{e}}^{i/5\pi }{a}^{1/10}\sqrt{x}\right)+\mathit{\_}\mathit{C}\mathit{4}{x}^{\frac{5}{2}}{\mathit{I}}_5\left(2{\mathrm{e}}^{2/5i\pi }{a}^{1/10}\sqrt{x}\right)+\mathit{\_}\mathit{C}\mathit{5}{x}^{\frac{5}{2}}{\mathit{I}}_5\left(2{\mathrm{e}}^{3/5i\pi }{a}^{1/10}\sqrt{x}\right)+\mathit{\_}\mathit{C}\mathit{6}{x}^{\frac{5}{2}}{\mathit{I}}_5\left(2{\mathrm{e}}^{4/5i\pi }{a}^{1/10}\sqrt{x}\right)+\mathit{\_}\mathit{C}\mathit{7}{x}^{\frac{5}{2}}{\mathit{Y}}_5\left(2i{\mathrm{e}}^{\frac{i}{5}\pi }{a}^{\frac{1}{10}}\sqrt{x}\right)+\mathit{\_}\mathit{C}\mathit{8}{x}^{\frac{5}{2}}{\mathit{Y}}_5\left(2i{\mathrm{e}}^{\frac{2i}{5}\pi }{a}^{\frac{1}{10}}\sqrt{x}\right)+\mathit{\_}\mathit{C}\mathit{9}{x}^{\frac{5}{2}}{\mathit{Y}}_5\left(2i{\mathrm{e}}^{\frac{3i}{5}\pi }{a}^{\frac{1}{10}}\sqrt{x}\right)+\mathit{\_}\mathit{C}\mathit{10}{x}^{\frac{5}{2}}{\mathit{Y}}_5\left(2i{\mathrm{e}}^{\frac{4i}{5}\pi }{a}^{\frac{1}{10}}\sqrt{x}\right)\}$$