80.6.20 problem 20

Internal problem ID [21310]
Book : A Textbook on Ordinary Differential Equations by Shair Ahmad and Antonio Ambrosetti. Second edition. ISBN 978-3-319-16407-6. Springer 2015
Section : Chapter 6. Higher order linear equations. Excercise 6.5 at page 133
Problem number : 20
Date solved : Thursday, October 02, 2025 at 07:28:18 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} x^{\left (5\right )}+x&=0 \end{align*}

With initial conditions

\begin{align*} x \left (\infty \right )&=0 \\ \end{align*}

✗ Maple

ode:=diff(diff(diff(diff(diff(x(t),t),t),t),t),t)+x(t) = 0; 
ic:=[x(infinity) = 0]; 
dsolve([ode,op(ic)],x(t), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[x[t],{t,5}]+x[t]==0; 
ic={x[Infinity]==0}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

{}

✗ Sympy

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(x(t) + Derivative(x(t), (t, 5)),0) 
ics = {x(oo): 0} 
dsolve(ode,func=x(t),ics=ics)
 

ValueError : Couldnt solve for initial conditions