80.6.7 problem 7

Internal problem ID [21297]
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 : 7
Date solved : Thursday, October 02, 2025 at 07:27:55 PM
CAS classification : [[_3rd_order, _missing_x]]

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

With initial conditions

\begin{align*} x \left (0\right )&=1 \\ x \left (\infty \right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.074 (sec). Leaf size: 15

ode:=diff(diff(diff(x(t),t),t),t)-diff(x(t),t) = 0; 
ic:=[x(0) = 1, x(infinity) = 0]; 
dsolve([ode,op(ic)],x(t), singsol=all);
 

\[ x = -c_3 +1+c_3 \,{\mathrm e}^{-t} \]

✓ Mathematica. Time used: 0.037 (sec). Leaf size: 10

ode=D[x[t],{t,3}]-D[x[t],t]==0; 
ic={x[0]==1,x[Infinity]==0}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to e^{-t} \end{align*}

✓ Sympy. Time used: 0.050 (sec). Leaf size: 19

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

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