80.6.12 problem 12

Internal problem ID [21302]
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 : 12
Date solved : Thursday, October 02, 2025 at 07:28:15 PM
CAS classification : [[_high_order, _missing_x]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 32

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

\[ x = c_1 \,{\mathrm e}^{t}+c_2 \,{\mathrm e}^{-t}+c_3 \,{\mathrm e}^{\sqrt {5}\, t}+c_4 \,{\mathrm e}^{-\sqrt {5}\, t} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 45

ode=D[x[t],{t,4}]-6*D[x[t],{t,2}]+5*x[t]==0; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to c_1 e^{\sqrt {5} t}+c_2 e^{-\sqrt {5} t}+c_3 e^{-t}+c_4 e^t \end{align*}

✓ Sympy. Time used: 0.061 (sec). Leaf size: 32

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(5*x(t) - 6*Derivative(x(t), (t, 2)) + Derivative(x(t), (t, 4)),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

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