Internal problem ID [2377]
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 3.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, class A]]
Solve \begin {gather*} \boxed {y^{\prime }+4 y-3 \left (\delta \left (t -1\right )\right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 19
dsolve([diff(y(t),t)+4*y(t)=3*Dirac(t-1),y(0) = 2],y(t), singsol=all)
\[ y \relax (t ) = 3 \theta \left (t -1\right ) {\mathrm e}^{-4 t +4}+2 \,{\mathrm e}^{-4 t} \]
✓ Solution by Mathematica
Time used: 0.032 (sec). Leaf size: 22
DSolve[{y'[t]+4*y[t]==3*DiracDelta[t-1],{y[0]==2}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to e^{-4 t} \left (3 e^4 \theta (t-1)+2\right ) \\ \end{align*}