80.6.4 problem 4

Internal problem ID [21294]
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 : 4
Date solved : Thursday, October 02, 2025 at 07:27:54 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} x^{\prime \prime \prime }-4 x^{\prime \prime }+x^{\prime }-4 x&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 19

ode:=diff(diff(diff(x(t),t),t),t)-4*diff(diff(x(t),t),t)+diff(x(t),t)-4*x(t) = 0; 
dsolve(ode,x(t), singsol=all);
 

\[ x = c_1 \,{\mathrm e}^{4 t}+c_2 \sin \left (t \right )+c_3 \cos \left (t \right ) \]

✓ Mathematica. Time used: 0.005 (sec). Leaf size: 24

ode=D[x[t],{t,3}]-4*D[x[t],{t,2}]+D[x[t],t]-4*x[t]==0; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to c_3 e^{4 t}+c_1 \cos (t)+c_2 \sin (t) \end{align*}

✓ Sympy. Time used: 0.076 (sec). Leaf size: 19

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(-4*x(t) + Derivative(x(t), t) - 4*Derivative(x(t), (t, 2)) + Derivative(x(t), (t, 3)),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

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