72.16.8 problem 8

Internal problem ID [14904]
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 : 8
Date solved : Tuesday, January 28, 2025 at 07:19:29 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+y^{\prime }-6 y&=4 \,{\mathrm e}^{-3 t} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 24

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

\[ y = \frac {\left (5 \,{\mathrm e}^{5 t} c_{1} +5 c_{2} -4 t \right ) {\mathrm e}^{-3 t}}{5} \]

✓ Solution by Mathematica

Time used: 0.038 (sec). Leaf size: 32

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

\[ y(t)\to \frac {1}{25} e^{-3 t} \left (-20 t+25 c_2 e^{5 t}-4+25 c_1\right ) \]