Internal problem ID [2376]
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 2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, class A]]
Solve \begin {gather*} \boxed {y^{\prime }-2 y-\left (\delta \left (t -2\right )\right )=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 18
dsolve([diff(y(t),t)-2*y(t)=Dirac(t-2),y(0) = 1],y(t), singsol=all)
\[ y \relax (t ) = \theta \left (t -2\right ) {\mathrm e}^{-4+2 t}+{\mathrm e}^{2 t} \]
✓ Solution by Mathematica
Time used: 0.034 (sec). Leaf size: 23
DSolve[{y'[t]-2*y[t]==DiracDelta[t-2],{y[0]==3}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to e^{2 t-4} \left (\theta (t-2)+3 e^4\right ) \\ \end{align*}