Internal problem ID [9912]
Internal file name [OUTPUT/8859_Monday_June_06_2022_05_41_23_AM_32680487/index.tex]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 5, linear fifth and higher order
Problem number: 1590.
ODE order: 5.
ODE degree: 1.
The type(s) of ODE detected by this program : "unknown"
Maple gives the following as the ode type
[[_high_order, _with_linear_symmetries]]
Unable to solve or complete the solution.
\[ \boxed {\left (x -a \right )^{5} \left (x -b \right )^{5} y^{\left (5\right )}-c y=0} \] Unable to solve this ODE.
Maple trace
`Methods for high order ODEs: --- Trying classification methods --- trying a quadrature checking if the LODE has constant coefficients checking if the LODE is of Euler type trying high order exact linear fully integrable trying to convert to a linear ODE with constant coefficients trying differential order: 5; missing the dependent variable trying a solution in terms of MeijerG functions trying reduction of order using simple exponentials trying differential order: 5; exact nonlinear --- Trying Lie symmetry methods, high order --- `, `-> Computing symmetries using: way = 3`[0, y], [a*b-a*x-b*x+x^2, 4*x*y]
✗ Solution by Maple
dsolve((x-a)^5*(x-b)^5*diff(y(x),x$5)-c*y(x)=0,y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[(x-a)^5*(x-b)^5*y'''''[x]-c*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
Timed out