80.6.5 problem 5

Internal problem ID [21295]
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 : 5
Date solved : Thursday, October 02, 2025 at 07:27:54 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} x^{\prime \prime \prime }-3 x^{\prime \prime }+4 x&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 21

ode:=diff(diff(diff(x(t),t),t),t)-3*diff(diff(x(t),t),t)+4*x(t) = 0; 
dsolve(ode,x(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 27

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

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

✓ Sympy. Time used: 0.052 (sec). Leaf size: 17

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

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