66.17.7 problem 7

Internal problem ID [16230]
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 4.2 page 412
Problem number : 7
Date solved : Thursday, October 02, 2025 at 10:43:53 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+4 y^{\prime }+13 y&=3 \cos \left (2 t \right ) \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 37

ode:=diff(diff(y(t),t),t)+4*diff(y(t),t)+13*y(t) = 3*cos(2*t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = {\mathrm e}^{-2 t} \sin \left (3 t \right ) c_2 +{\mathrm e}^{-2 t} \cos \left (3 t \right ) c_1 +\frac {27 \cos \left (2 t \right )}{145}+\frac {24 \sin \left (2 t \right )}{145} \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 47

ode=D[y[t],{t,2}]+4*D[y[t],t]+13*y[t]==3*Cos[2*t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {3}{145} (8 \sin (2 t)+9 \cos (2 t))+c_2 e^{-2 t} \cos (3 t)+c_1 e^{-2 t} \sin (3 t) \end{align*}

✓ Sympy. Time used: 0.155 (sec). Leaf size: 37

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(13*y(t) - 3*cos(2*t) + 4*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \left (C_{1} \sin {\left (3 t \right )} + C_{2} \cos {\left (3 t \right )}\right ) e^{- 2 t} + \frac {24 \sin {\left (2 t \right )}}{145} + \frac {27 \cos {\left (2 t \right )}}{145} \]