72.17.6 problem 6

Internal problem ID [14863]
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 : 6
Date solved : Thursday, March 13, 2025 at 05:13:50 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+6 y^{\prime }+8 y&=-4 \cos \left (3 t \right ) \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 30

ode:=diff(diff(y(t),t),t)+6*diff(y(t),t)+8*y(t) = -4*cos(3*t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = -\frac {{\mathrm e}^{-4 t} c_{1}}{2}+{\mathrm e}^{-2 t} c_{2} -\frac {72 \sin \left (3 t \right )}{325}+\frac {4 \cos \left (3 t \right )}{325} \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 37

ode=D[y[t],{t,2}]+6*D[y[t],t]+8*y[t]==-4*Cos[3*t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to c_1 e^{-4 t}+c_2 e^{-2 t}+\frac {4}{325} (\cos (3 t)-18 \sin (3 t)) \]

✓ Sympy. Time used: 0.217 (sec). Leaf size: 32

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(8*y(t) + 4*cos(3*t) + 6*Derivative(y(t), t) + Derivative(y(t), (t, 2)),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = C_{1} e^{- 4 t} + C_{2} e^{- 2 t} - \frac {72 \sin {\left (3 t \right )}}{325} + \frac {4 \cos {\left (3 t \right )}}{325} \]