Internal problem ID [2375]
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 1.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, class A]]
Solve \begin {gather*} \boxed {y^{\prime }+y-\left (\delta \left (t -5\right )\right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 3] \end {align*}
✓ Solution by Maple
Time used: 0.012 (sec). Leaf size: 18
dsolve([diff(y(t),t)+y(t)=Dirac(t-5),y(0) = 3],y(t), singsol=all)
\[ y \relax (t ) = \theta \left (t -5\right ) {\mathrm e}^{-t +5}+3 \,{\mathrm e}^{-t} \]
✓ Solution by Mathematica
Time used: 0.039 (sec). Leaf size: 21
DSolve[{y'[t]+y[t]==DiracDelta[t-5],{y[0]==3}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to e^{-t} \left (e^5 \theta (t-5)+3\right ) \\ \end{align*}