72.16.5 problem 5

Internal problem ID [14901]
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 4.1 page 399
Problem number : 5
Date solved : Tuesday, January 28, 2025 at 07:19:21 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+4 y^{\prime }+13 y&=-3 \,{\mathrm e}^{-2 t} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 26

dsolve(diff(y(t),t$2)+4*diff(y(t),t)+13*y(t)=-3*exp(-2*t),y(t), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 32

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

\[ y(t)\to \frac {1}{3} e^{-2 t} (3 c_2 \cos (3 t)+3 c_1 \sin (3 t)-1) \]