80.6.11 problem 11

Internal problem ID [21301]
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 : 11
Date solved : Friday, October 03, 2025 at 07:49:36 AM
CAS classification : [[_3rd_order, _missing_x]]

\begin{align*} x^{\prime \prime \prime }-3 x^{\prime }+k x&=0 \end{align*}

With initial conditions

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

✓ Maple. Time used: 14.385 (sec). Leaf size: 597

ode:=diff(diff(diff(x(t),t),t),t)-3*diff(x(t),t)+k*x(t) = 0; 
ic:=[x(0) = 1, x(infinity) = 0]; 
dsolve([ode,op(ic)],x(t), singsol=all);
 

\begin{align*} \text {Solution too large to show}\end{align*}

✗ Mathematica

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

{}

✗ Sympy

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

False