71.16.1 problem 1

Internal problem ID [14550]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 5. The Laplace Transform Method. Exercises 5.5, page 273
Problem number : 1
Date solved : Tuesday, January 28, 2025 at 06:43:19 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+3 y&=\delta \left (x -2\right ) \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 9.457 (sec). Leaf size: 20

dsolve([diff(y(x),x)+3*y(x)=Dirac(x-2),y(0) = 1],y(x), singsol=all)
 

\[ y = \operatorname {Heaviside}\left (x -2\right ) {\mathrm e}^{6-3 x}+{\mathrm e}^{-3 x} \]

✓ Solution by Mathematica

Time used: 0.034 (sec). Leaf size: 29

DSolve[{D[y[x],x]+3*y[x]==DiracDelta[x-2],{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-3 x} \left (\int _0^xe^6 \delta (K[1]-2)dK[1]+1\right ) \]