85.67.16 problem 16

Internal problem ID [22907]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 4. Linear differential equations. A Exercises at page 216
Problem number : 16
Date solved : Thursday, October 02, 2025 at 09:16:30 PM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} s^{\prime \prime \prime \prime }-2 s^{\prime \prime }+s&=100 \cos \left (3 t \right ) \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 27

ode:=diff(diff(diff(diff(s(t),t),t),t),t)-2*diff(diff(s(t),t),t)+s(t) = 100*cos(3*t); 
dsolve(ode,s(t), singsol=all);
 

\[ s = \left (c_4 t +c_2 \right ) {\mathrm e}^{-t}+\left (c_3 t +c_1 \right ) {\mathrm e}^{t}+\cos \left (3 t \right ) \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 40

ode=D[s[t],{t,4}]-2*D[s[t],{t,2}]+s[t]==100*Cos[3*t]; 
ic={}; 
DSolve[{ode,ic},s[t],t,IncludeSingularSolutions->True]
 

\begin{align*} s(t)&\to \cos (3 t)+e^{-t} \left (c_2 t+c_3 e^{2 t}+c_4 e^{2 t} t+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.064 (sec). Leaf size: 24

from sympy import * 
t = symbols("t") 
s = Function("s") 
ode = Eq(s(t) - 100*cos(3*t) - 2*Derivative(s(t), (t, 2)) + Derivative(s(t), (t, 4)),0) 
ics = {} 
dsolve(ode,func=s(t),ics=ics)
 

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