\[ a \nu x^{\nu -1} y(x)+a x^{\nu } y'(x)+y^{(5)}(x)=0 \] ✓ Mathematica : cpu = 0.107851 (sec), leaf count = 787
\[\left \{\left \{y(x)\to c_5 \left (\frac {4}{\nu }+1\right )^{-\frac {16}{\nu +4}} \nu ^{-\frac {16}{\nu +4}} a^{\frac {4}{\nu +4}} \left (x^{\nu }\right )^{\frac {4 \left (\frac {4}{\nu }+1\right )}{\nu +4}} \, _1F_4\left (\frac {4}{\nu \left (1+\frac {4}{\nu }\right )}+\frac {1}{1+\frac {4}{\nu }};1+\frac {1}{\left (1+\frac {4}{\nu }\right ) \nu },1+\frac {2}{\left (1+\frac {4}{\nu }\right ) \nu },1+\frac {3}{\left (1+\frac {4}{\nu }\right ) \nu },1+\frac {4}{\left (1+\frac {4}{\nu }\right ) \nu };-\frac {a \left (x^{\nu }\right )^{1+\frac {4}{\nu }}}{\left (1+\frac {4}{\nu }\right )^4 \nu ^4}\right )+c_4 \left (\frac {4}{\nu }+1\right )^{-\frac {12}{\nu +4}} \nu ^{-\frac {12}{\nu +4}} a^{\frac {3}{\nu +4}} \left (x^{\nu }\right )^{\frac {3 \left (\frac {4}{\nu }+1\right )}{\nu +4}} \, _1F_4\left (\frac {3}{\nu \left (1+\frac {4}{\nu }\right )}+\frac {1}{1+\frac {4}{\nu }};1-\frac {1}{\left (1+\frac {4}{\nu }\right ) \nu },1+\frac {1}{\left (1+\frac {4}{\nu }\right ) \nu },1+\frac {2}{\left (1+\frac {4}{\nu }\right ) \nu },1+\frac {3}{\left (1+\frac {4}{\nu }\right ) \nu };-\frac {a \left (x^{\nu }\right )^{1+\frac {4}{\nu }}}{\left (1+\frac {4}{\nu }\right )^4 \nu ^4}\right )+c_3 \left (\frac {4}{\nu }+1\right )^{-\frac {8}{\nu +4}} \nu ^{-\frac {8}{\nu +4}} a^{\frac {2}{\nu +4}} \left (x^{\nu }\right )^{\frac {2 \left (\frac {4}{\nu }+1\right )}{\nu +4}} \, _1F_4\left (\frac {2}{\nu \left (1+\frac {4}{\nu }\right )}+\frac {1}{1+\frac {4}{\nu }};1-\frac {2}{\left (1+\frac {4}{\nu }\right ) \nu },1-\frac {1}{\left (1+\frac {4}{\nu }\right ) \nu },1+\frac {1}{\left (1+\frac {4}{\nu }\right ) \nu },1+\frac {2}{\left (1+\frac {4}{\nu }\right ) \nu };-\frac {a \left (x^{\nu }\right )^{1+\frac {4}{\nu }}}{\left (1+\frac {4}{\nu }\right )^4 \nu ^4}\right )+c_2 \left (\frac {4}{\nu }+1\right )^{-\frac {4}{\nu +4}} \nu ^{-\frac {4}{\nu +4}} a^{\frac {1}{\nu +4}} \left (x^{\nu }\right )^{\frac {\frac {4}{\nu }+1}{\nu +4}} \, _1F_4\left (\frac {1}{\nu \left (1+\frac {4}{\nu }\right )}+\frac {1}{1+\frac {4}{\nu }};1-\frac {3}{\left (1+\frac {4}{\nu }\right ) \nu },1-\frac {2}{\left (1+\frac {4}{\nu }\right ) \nu },1-\frac {1}{\left (1+\frac {4}{\nu }\right ) \nu },1+\frac {1}{\left (1+\frac {4}{\nu }\right ) \nu };-\frac {a \left (x^{\nu }\right )^{1+\frac {4}{\nu }}}{\left (1+\frac {4}{\nu }\right )^4 \nu ^4}\right )+c_1 \, _1F_4\left (\frac {1}{1+\frac {4}{\nu }};1-\frac {4}{\left (1+\frac {4}{\nu }\right ) \nu },1-\frac {3}{\left (1+\frac {4}{\nu }\right ) \nu },1-\frac {2}{\left (1+\frac {4}{\nu }\right ) \nu },1-\frac {1}{\left (1+\frac {4}{\nu }\right ) \nu };-\frac {a \left (x^{\nu }\right )^{1+\frac {4}{\nu }}}{\left (1+\frac {4}{\nu }\right )^4 \nu ^4}\right )\right \}\right \}\] ✗ Maple : cpu = 0. (sec), leaf count = 0
, result contains DESol or ODESolStruc
\[y \relax (x ) = \mathit {DESol}\left (\left \{\frac {d^{5}}{d x^{5}}\textit {\_Y} \relax (x )+a \,x^{\nu } \left (\frac {d}{d x}\textit {\_Y} \relax (x )\right )+a \nu \,x^{\nu -1} \textit {\_Y} \relax (x )\right \}, \left \{\textit {\_Y} \relax (x )\right \}\right )\]