80.5.35 problem C 11

Internal problem ID [21256]
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 5. Second order equations. Excercise 5.9 at page 119
Problem number : C 11
Date solved : Thursday, October 02, 2025 at 07:27:23 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 21

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

\[ x = \sin \left (2 t \right ) c_2 +\cos \left (2 t \right ) c_1 +\frac {\cos \left (t \right )}{3} \]

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 26

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

\begin{align*} x(t)&\to \frac {\cos (t)}{3}+c_1 \cos (2 t)+c_2 \sin (2 t) \end{align*}

✓ Sympy. Time used: 0.038 (sec). Leaf size: 20

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

\[ x{\left (t \right )} = C_{1} \sin {\left (2 t \right )} + C_{2} \cos {\left (2 t \right )} + \frac {\cos {\left (t \right )}}{3} \]