80.6.28 problem 31

Internal problem ID [21318]
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 : 31
Date solved : Thursday, October 02, 2025 at 07:28:24 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} x^{\prime \prime \prime \prime }-3 x^{\prime \prime \prime }+2 x^{\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)-3*diff(diff(diff(x(t),t),t),t)+2*diff(x(t),t)-5*x(t) = 0; 
dsolve(ode,x(t), singsol=all);
 

\[ x = \moverset {4}{\munderset {\textit {\_a} =1}{\sum }}{\mathrm e}^{\operatorname {RootOf}\left (\textit {\_Z}^{4}-3 \textit {\_Z}^{3}+2 \textit {\_Z} -5, \operatorname {index} =\textit {\_a} \right ) t} \textit {\_C}_{\textit {\_a}} \]

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 114

ode=D[x[t],{t,4}]-3*D[x[t],{t,3}]+2*D[x[t],t]-5*x[t]==0; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to c_3 \exp \left (t \text {Root}\left [\text {$\#$1}^4-3 \text {$\#$1}^3+2 \text {$\#$1}-5\&,3\right ]\right )+c_4 \exp \left (t \text {Root}\left [\text {$\#$1}^4-3 \text {$\#$1}^3+2 \text {$\#$1}-5\&,4\right ]\right )+c_1 \exp \left (t \text {Root}\left [\text {$\#$1}^4-3 \text {$\#$1}^3+2 \text {$\#$1}-5\&,1\right ]\right )+c_2 \exp \left (t \text {Root}\left [\text {$\#$1}^4-3 \text {$\#$1}^3+2 \text {$\#$1}-5\&,2\right ]\right ) \end{align*}

✓ Sympy. Time used: 1.518 (sec). Leaf size: 592

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(-5*x(t) + 2*Derivative(x(t), t) - 3*Derivative(x(t), (t, 3)) + Derivative(x(t), (t, 4)),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

\[ \text {Solution too large to show} \]