60.6.4 problem 1581

Internal problem ID [11541]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 5, linear fifth and higher order
Problem number : 1581
Date solved : Wednesday, March 05, 2025 at 02:27:35 PM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

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