80.6.1 problem 1

Internal problem ID [21291]
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 : 1
Date solved : Thursday, October 02, 2025 at 07:27:53 PM
CAS classification : [[_3rd_order, _quadrature]]

\begin{align*} 2 x^{\prime \prime \prime }&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 15

ode:=2*diff(diff(diff(x(t),t),t),t) = 0; 
dsolve(ode,x(t), singsol=all);
 

\[ x = \frac {1}{2} c_1 \,t^{2}+c_2 t +c_3 \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 17

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

\begin{align*} x(t)&\to t (c_3 t+c_2)+c_1 \end{align*}

✓ Sympy. Time used: 0.026 (sec). Leaf size: 12

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

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