Internal problem ID [2884]
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`]]
\[ \boxed {y^{\prime }+y=\delta \left (t -5\right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 3] \end {align*}
✓ Solution by Maple
Time used: 2.219 (sec). Leaf size: 22
dsolve([diff(y(t),t)+y(t)=Dirac(t-5),y(0) = 3],y(t), singsol=all)
\[ y \left (t \right ) = \operatorname {Heaviside}\left (t -5\right ) {\mathrm e}^{-t +5}+3 \,{\mathrm e}^{-t} \]
✓ Solution by Mathematica
Time used: 0.029 (sec). Leaf size: 21
DSolve[{y'[t]+y[t]==DiracDelta[t-5],{y[0]==3}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to e^{-t} \left (e^5 \theta (t-5)+3\right ) \]