Internal problem ID [9167]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 5, linear fifth and higher order
Problem number: 1588.
ODE order: 5.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x^{10} y^{\relax (5)}-a y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 90
dsolve(x^10*diff(diff(diff(diff(diff(y(x),x),x),x),x),x)-a*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} \hypergeom \left (\left [\right ], \left [\frac {6}{5}, \frac {7}{5}, \frac {8}{5}, \frac {9}{5}\right ], -\frac {a}{3125 x^{5}}\right )+c_{2} x \hypergeom \left (\left [\right ], \left [\frac {4}{5}, \frac {6}{5}, \frac {7}{5}, \frac {8}{5}\right ], -\frac {a}{3125 x^{5}}\right )+c_{3} x^{2} \hypergeom \left (\left [\right ], \left [\frac {3}{5}, \frac {4}{5}, \frac {6}{5}, \frac {7}{5}\right ], -\frac {a}{3125 x^{5}}\right )+c_{4} x^{3} \hypergeom \left (\left [\right ], \left [\frac {2}{5}, \frac {3}{5}, \frac {4}{5}, \frac {6}{5}\right ], -\frac {a}{3125 x^{5}}\right )+c_{5} x^{4} \hypergeom \left (\left [\right ], \left [\frac {1}{5}, \frac {2}{5}, \frac {3}{5}, \frac {4}{5}\right ], -\frac {a}{3125 x^{5}}\right ) \]
✓ Solution by Mathematica
Time used: 7.159 (sec). Leaf size: 103
DSolve[x^10*y'''''[x]-a*y[x]== 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x^4 \left (c_1 e^{-\frac {\sqrt [5]{a}}{x}}+c_2 e^{\frac {\sqrt [5]{-1} \sqrt [5]{a}}{x}}+c_3 e^{-\frac {(-1)^{2/5} \sqrt [5]{a}}{x}}+c_4 e^{\frac {(-1)^{3/5} \sqrt [5]{a}}{x}}+c_5 e^{-\frac {(-1)^{4/5} \sqrt [5]{a}}{x}}\right ) \\ \end{align*}