20.23.4 problem Problem 4

Internal problem ID [3976]
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
Date solved : Monday, January 27, 2025 at 08:05:32 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }-5 y&=2 \,{\mathrm e}^{-t}+\delta \left (t -3\right ) \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 3.662 (sec). Leaf size: 26

dsolve([diff(y(t),t)-5*y(t)=2*exp(-t)+Dirac(t-3),y(0) = 0],y(t), singsol=all)
 

\[ y = \frac {2 \,{\mathrm e}^{2 t} \sinh \left (3 t \right )}{3}+\operatorname {Heaviside}\left (t -3\right ) {\mathrm e}^{5 t -15} \]

✓ Solution by Mathematica

Time used: 0.098 (sec). Leaf size: 34

DSolve[{D[y[t],t]-5*y[t]==2*Exp[-t]+DiracDelta[t-3],{y[0]==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{3} e^{-t} \left (3 e^{6 t-15} \theta (t-3)+e^{6 t}-1\right ) \]