80.6.16 problem 16

Internal problem ID [21306]
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 : 16
Date solved : Thursday, October 02, 2025 at 07:28:16 PM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} x^{\prime \prime \prime \prime }-8 x^{\prime \prime \prime }+23 x^{\prime \prime }-28 x^{\prime }+12 x&=0 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.054 (sec). Leaf size: 12

ode:=diff(diff(diff(diff(x(t),t),t),t),t)-8*diff(diff(diff(x(t),t),t),t)+23*diff(diff(x(t),t),t)-28*diff(x(t),t)+12*x(t) = 0; 
ic:=[x(infinity) = 0]; 
dsolve([ode,op(ic)],x(t), singsol=all);
 

\[ x = -\operatorname {signum}\left (c_2 \,{\mathrm e}^{t}\right ) \infty \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 6

ode=D[x[t],{t,4}]-8*D[x[t],{t,3}]+23*D[x[t],{t,2}]-28*D[x[t],t]+12*x[t]==0; 
ic={x[Infinity]==0}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to 0 \end{align*}

✓ Sympy. Time used: 0.127 (sec). Leaf size: 31

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(12*x(t) - 28*Derivative(x(t), t) + 23*Derivative(x(t), (t, 2)) - 8*Derivative(x(t), (t, 3)) + Derivative(x(t), (t, 4)),0) 
ics = {x(oo): 0} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = \left (- \infty C_{2} - \infty C_{3} + C_{4} e^{2 t} - \infty C_{4} + \left (C_{2} + C_{3} t\right ) e^{t}\right ) e^{t} \]