\[ x^5 y^{(10)}(x)-a y(x)=0 \] ✓ Mathematica : cpu = 0.377714 (sec), leaf count = 492
\[\left \{\left \{y(x)\to \frac {(-1)^{4/5} a^{9/5} c_1 x^9 \, _0F_9\left (;\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}\right )}{3814697265625}+\frac {(-1)^{3/5} a^{8/5} c_3 x^8 \, _0F_9\left (;\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}\right )}{152587890625}+\frac {(-1)^{2/5} a^{7/5} c_5 x^7 \, _0F_9\left (;\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}\right )}{6103515625}+\frac {\sqrt [5]{-1} a^{6/5} c_7 x^6 \, _0F_9\left (;\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}\right )}{244140625}+\frac {a c_9 x^5 \, _0F_9\left (;\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}\right )}{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 \}\right \}\]
✓ Maple : cpu = 0.939 (sec), leaf count = 174
\[ \left \{ y \left ( x \right ) ={x}^{{\frac {5}{2}}} \left ( {\it \_C2}\,{{\sl Y}_{5}\left (2\,i{a}^{{\frac {1}{10}}}\sqrt {x}\right )}+{\it \_C1}\,{{\sl I}_{5}\left (2\,{a}^{1/10}\sqrt {x}\right )}+{\it \_C6}\,{{\sl I}_{5}\left (2\,{{\rm e}^{4/5\,i\pi }}{a}^{1/10}\sqrt {x}\right )}+{\it \_C3}\,{{\sl I}_{5}\left (2\,{{\rm e}^{i/5\pi }}{a}^{1/10}\sqrt {x}\right )}+{\it \_C8}\,{{\sl Y}_{5}\left (2\,i{{\rm e}^{{\frac {2\,i}{5}}\pi }}{a}^{{\frac {1}{10}}}\sqrt {x}\right )}+{\it \_C7}\,{{\sl Y}_{5}\left (2\,i{{\rm e}^{{\frac {i}{5}}\pi }}{a}^{{\frac {1}{10}}}\sqrt {x}\right )}+{\it \_C10}\,{{\sl Y}_{5}\left (2\,i{{\rm e}^{{\frac {4\,i}{5}}\pi }}{a}^{{\frac {1}{10}}}\sqrt {x}\right )}+{\it \_C5}\,{{\sl I}_{5}\left (2\,{{\rm e}^{3/5\,i\pi }}{a}^{1/10}\sqrt {x}\right )}+{\it \_C4}\,{{\sl I}_{5}\left (2\,{{\rm e}^{2/5\,i\pi }}{a}^{1/10}\sqrt {x}\right )}+{\it \_C9}\,{{\sl Y}_{5}\left (2\,i{{\rm e}^{{\frac {3\,i}{5}}\pi }}{a}^{{\frac {1}{10}}}\sqrt {x}\right )} \right ) \right \} \]