72.17.6 problem 6

Internal problem ID [14942]
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 : Tuesday, January 28, 2025 at 07:21:30 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*}

✓ Solution by Maple

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

dsolve(diff(y(t),t$2)+6*diff(y(t),t)+8*y(t)=-4*cos(3*t),y(t), singsol=all)
 

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

✓ Solution by Mathematica

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

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

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