72.18.5 problem 5

Internal problem ID [14879]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 4. Forcing and Resonance. Section 4.3 page 424
Problem number : 5
Date solved : Thursday, March 13, 2025 at 05:18:12 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+9 y&=2 \cos \left (3 t \right ) \end{align*}

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

ode:=diff(diff(y(t),t),t)+9*y(t) = 2*cos(3*t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \frac {\left (9 c_{1} +1\right ) \cos \left (3 t \right )}{9}+\frac {\sin \left (3 t \right ) \left (t +3 c_{2} \right )}{3} \]

✓ Mathematica. Time used: 0.036 (sec). Leaf size: 64

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

\[ y(t)\to \sin (3 t) \int _1^t\frac {2}{3} \cos ^2(3 K[2])dK[2]+\cos (3 t) \int _1^t-\frac {1}{3} \sin (6 K[1])dK[1]+c_1 \cos (3 t)+c_2 \sin (3 t) \]

✓ Sympy. Time used: 0.092 (sec). Leaf size: 19

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

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