80.6.19 problem 19

Internal problem ID [21309]
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 : 19
Date solved : Thursday, October 02, 2025 at 07:28:17 PM
CAS classification : [[_high_order, _missing_x]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 27

ode:=diff(diff(diff(diff(diff(x(t),t),t),t),t),t)+diff(diff(diff(diff(x(t),t),t),t),t)-diff(x(t),t)-x(t) = 0; 
dsolve(ode,x(t), singsol=all);
 

\[ x = c_1 \,{\mathrm e}^{t}+\left (c_3 t +c_2 \right ) {\mathrm e}^{-t}+c_4 \sin \left (t \right )+c_5 \cos \left (t \right ) \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 40

ode=D[x[t],{t,5}]+D[x[t],{t,4}]-D[x[t],t]-x[t]==0; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to c_1 \cos (t)+e^{-t} \left (c_4 t+c_5 e^{2 t}+c_2 e^t \sin (t)+c_3\right ) \end{align*}

✓ Sympy. Time used: 0.104 (sec). Leaf size: 26

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(-x(t) - Derivative(x(t), t) + Derivative(x(t), (t, 4)) + Derivative(x(t), (t, 5)),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = C_{3} e^{t} + C_{4} \sin {\left (t \right )} + C_{5} \cos {\left (t \right )} + \left (C_{1} + C_{2} t\right ) e^{- t} \]