72.16.2 problem 2

Internal problem ID [14898]
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 : 2
Date solved : Tuesday, January 28, 2025 at 07:19:07 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+6 y^{\prime }+8 y&=2 \,{\mathrm e}^{-3 t} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 26

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

\[ y = -\frac {\left (c_{1} {\mathrm e}^{-2 t}+4 \,{\mathrm e}^{-t}-2 c_{2} \right ) {\mathrm e}^{-2 t}}{2} \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 27

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

\[ y(t)\to e^{-4 t} \left (-2 e^t+c_2 e^{2 t}+c_1\right ) \]