54.6.13 problem 1590

Internal problem ID [12849]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 5, linear fifth and higher order
Problem number : 1590
Date solved : Wednesday, October 01, 2025 at 02:22:30 AM
CAS classification : [[_high_order, _with_linear_symmetries]]

\begin{align*} \left (x -a \right )^{5} \left (x -b \right )^{5} y^{\left (5\right )}-c y&=0 \end{align*}

✗ Maple

ode:=(x-a)^5*(x-b)^5*diff(diff(diff(diff(diff(y(x),x),x),x),x),x)-c*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=(x-a)^5*(x-b)^5*D[y[x],{x,5}]-c*y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Timed out

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
b = symbols("b") 
c = symbols("c") 
y = Function("y") 
ode = Eq(-c*y(x) + (-a + x)**5*(-b + x)**5*Derivative(y(x), (x, 5)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : solve: Cannot solve -c*y(x) + (-a + x)**5*(-b + x)**5*Derivative(y(x), (x, 5))