80.5.45 problem C 21

Internal problem ID [21266]
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 21
Date solved : Thursday, October 02, 2025 at 07:27:29 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{\prime \prime }+4 x&=\sin \left (2 t \right ) \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 24

ode:=diff(diff(x(t),t),t)+4*x(t) = sin(2*t); 
dsolve(ode,x(t), singsol=all);
 

\[ x = \frac {\left (4 c_1 -t \right ) \cos \left (2 t \right )}{4}+\sin \left (2 t \right ) c_2 \]

✓ Mathematica. Time used: 0.031 (sec). Leaf size: 33

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

\begin{align*} x(t)&\to \left (-\frac {t}{4}+c_1\right ) \cos (2 t)+\frac {1}{8} (1+16 c_2) \sin (t) \cos (t) \end{align*}

✓ Sympy. Time used: 0.057 (sec). Leaf size: 19

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

\[ x{\left (t \right )} = C_{2} \sin {\left (2 t \right )} + \left (C_{1} - \frac {t}{4}\right ) \cos {\left (2 t \right )} \]