80.6.25 problem 25

Internal problem ID [21315]
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 : 25
Date solved : Thursday, October 02, 2025 at 07:28:23 PM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} x^{\prime \prime \prime }-x^{\prime \prime }&=1 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 18

ode:=diff(diff(diff(x(t),t),t),t)-diff(diff(x(t),t),t) = 1; 
dsolve(ode,x(t), singsol=all);
 

\[ x = {\mathrm e}^{t} c_1 -\frac {t^{2}}{2}+c_2 t +c_3 \]

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 25

ode=D[x[t],{t,3}]-D[x[t],{t,2}]==1; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to -\frac {t^2}{2}+c_3 t+c_1 e^t+c_2 \end{align*}

✓ Sympy. Time used: 0.034 (sec). Leaf size: 17

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(-Derivative(x(t), (t, 2)) + Derivative(x(t), (t, 3)) - 1,0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

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