Internal problem ID [2887]
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`]]
\[ \boxed {y^{\prime }-5 y=2 \,{\mathrm e}^{-t}+\delta \left (t -3\right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 2.578 (sec). Leaf size: 32
dsolve([diff(y(t),t)-5*y(t)=2*exp(-t)+Dirac(t-3),y(0) = 0],y(t), singsol=all)
\[ y \left (t \right ) = \frac {2 \,{\mathrm e}^{2 t} \sinh \left (3 t \right )}{3}+\operatorname {Heaviside}\left (-3+t \right ) {\mathrm e}^{5 t -15} \]
✓ Solution by Mathematica
Time used: 0.093 (sec). Leaf size: 34
DSolve[{y'[t]-5*y[t]==2*Exp[-t]+DiracDelta[t-3],{y[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{3} e^{-t} \left (3 e^{6 t-15} \theta (t-3)+e^{6 t}-1\right ) \]