80.6.3 problem 3

Internal problem ID [21293]
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 : 3
Date solved : Thursday, October 02, 2025 at 07:27:54 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} x^{\prime \prime \prime }+5 x^{\prime \prime }-6 x&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 30

ode:=diff(diff(diff(x(t),t),t),t)+5*diff(diff(x(t),t),t)-6*x(t) = 0; 
dsolve(ode,x(t), singsol=all);
 

\[ x = c_1 \,{\mathrm e}^{t}+c_2 \,{\mathrm e}^{\left (-3+\sqrt {3}\right ) t}+c_3 \,{\mathrm e}^{-\left (3+\sqrt {3}\right ) t} \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 41

ode=D[x[t],{t,3}]+5*D[x[t],{t,2}]-6*x[t]==0; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to c_1 e^{-\left (\left (3+\sqrt {3}\right ) t\right )}+c_2 e^{\left (\sqrt {3}-3\right ) t}+c_3 e^t \end{align*}

✓ Sympy. Time used: 0.071 (sec). Leaf size: 32

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(-6*x(t) + 5*Derivative(x(t), (t, 2)) + Derivative(x(t), (t, 3)),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

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