80.6.23 problem 23

Internal problem ID [21313]
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 : 23
Date solved : Thursday, October 02, 2025 at 07:28:22 PM
CAS classification : [[_high_order, _missing_y]]

\begin{align*} x^{\prime \prime \prime \prime }+3 x^{\prime \prime \prime }+2 x^{\prime \prime }&={\mathrm e}^{t} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 26

ode:=diff(diff(diff(diff(x(t),t),t),t),t)+3*diff(diff(diff(x(t),t),t),t)+2*diff(diff(x(t),t),t) = exp(t); 
dsolve(ode,x(t), singsol=all);
 

\[ x = -\frac {{\mathrm e}^{-2 t} c_1}{4}+{\mathrm e}^{-t} c_2 +\frac {{\mathrm e}^{t}}{6}+c_3 t +c_4 \]

✓ Mathematica. Time used: 0.045 (sec). Leaf size: 38

ode=D[x[t],{t,4}]+3*D[x[t],{t,3}]+2*D[x[t],{t,2}]==Exp[t]; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to \frac {e^t}{6}+\frac {1}{4} c_1 e^{-2 t}+c_2 e^{-t}+c_4 t+c_3 \end{align*}

✓ Sympy. Time used: 0.061 (sec). Leaf size: 24

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(-exp(t) + 2*Derivative(x(t), (t, 2)) + 3*Derivative(x(t), (t, 3)) + Derivative(x(t), (t, 4)),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = C_{1} + C_{2} t + C_{3} e^{- 2 t} + C_{4} e^{- t} + \frac {e^{t}}{6} \]