90.18.9 problem 13

Internal problem ID [25281]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 4. Linear Constant Coefficient Differential Equations. Exercises at page 299
Problem number : 13
Date solved : Thursday, October 02, 2025 at 11:59:33 PM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=4 \cos \left (t \right ) \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 27

ode:=diff(diff(diff(y(t),t),t),t)-diff(diff(y(t),t),t)+diff(y(t),t)-y(t) = 4*cos(t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \left (-t +c_1 -2\right ) \cos \left (t \right )+\left (-t +c_3 +1\right ) \sin \left (t \right )+c_2 \,{\mathrm e}^{t} \]

✓ Mathematica. Time used: 0.006 (sec). Leaf size: 32

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

\begin{align*} y(t)&\to c_3 e^t+(-t-2+c_1) \cos (t)+(-t+1+c_2) \sin (t) \end{align*}

✓ Sympy. Time used: 0.129 (sec). Leaf size: 20

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

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