Internal problem ID [2378]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 10, The Laplace Transform and Some Elementary Applications. Exercises for 10.8.
page 710
Problem number: Problem 4.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, class A]]
Solve \begin {gather*} \boxed {y^{\prime }-5 y-2 \,{\mathrm e}^{-t}-\left (\delta \left (t -3\right )\right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.02 (sec). Leaf size: 24
dsolve([diff(y(t),t)-5*y(t)=2*exp(-t)+Dirac(t-3),y(0) = 0],y(t), singsol=all)
\[ y \relax (t ) = \frac {{\mathrm e}^{5 t}}{3}+\theta \left (t -3\right ) {\mathrm e}^{5 t -15}-\frac {{\mathrm e}^{-t}}{3} \]
✓ Solution by Mathematica
Time used: 0.091 (sec). Leaf size: 34
DSolve[{y'[t]-5*y[t]==2*Exp[-t]+DiracDelta[t-3],{y[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {1}{3} e^{-t} \left (3 e^{6 t-15} \theta (t-3)+e^{6 t}-1\right ) \\ \end{align*}