80.5.47 problem C 23

Internal problem ID [21268]
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 23
Date solved : Thursday, October 02, 2025 at 07:27:30 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{\prime \prime }+9 x&=\sin \left (t \right )+\sin \left (3 t \right ) \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 33

ode:=diff(diff(x(t),t),t)+9*x(t) = sin(t)+sin(3*t); 
dsolve(ode,x(t), singsol=all);
 

\[ x = \frac {\left (-t +6 c_1 \right ) \cos \left (3 t \right )}{6}+\frac {\left (36 c_2 +1\right ) \sin \left (3 t \right )}{36}+\frac {\sin \left (t \right )}{8} \]

✓ Mathematica. Time used: 0.124 (sec). Leaf size: 39

ode=D[x[t],{t,2}]+9*x[t]== Sin[t]+Sin[3*t]; 
ic={}; 
DSolve[{ode,ic},x[t],t,IncludeSingularSolutions->True]
 

\begin{align*} x(t)&\to \frac {\sin (t)}{8}+\left (-\frac {t}{6}+c_1\right ) \cos (3 t)+\frac {1}{12} (1+12 c_2) \sin (3 t) \end{align*}

✓ Sympy. Time used: 0.063 (sec). Leaf size: 24

from sympy import * 
t = symbols("t") 
x = Function("x") 
ode = Eq(9*x(t) - sin(t) - sin(3*t) + Derivative(x(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=x(t),ics=ics)
 

\[ x{\left (t \right )} = C_{2} \sin {\left (3 t \right )} + \left (C_{1} - \frac {t}{6}\right ) \cos {\left (3 t \right )} + \frac {\sin {\left (t \right )}}{8} \]