20.22.1 problem Problem 27

Internal problem ID [3956]
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 10.7. page 704
Problem number : Problem 27
Date solved : Monday, January 27, 2025 at 08:04:58 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+2 y&=2 \operatorname {Heaviside}\left (t -1\right ) \end{align*}

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 3.553 (sec). Leaf size: 25

dsolve([diff(y(t),t)+2*y(t)=2*Heaviside(t-1),y(0) = 1],y(t), singsol=all)
 

\[ y = -\operatorname {Heaviside}\left (-1+t \right ) {\mathrm e}^{2-2 t}+\operatorname {Heaviside}\left (-1+t \right )+{\mathrm e}^{-2 t} \]

✓ Solution by Mathematica

Time used: 0.048 (sec). Leaf size: 26

DSolve[{D[y[t],t]-y[t]==2*UnitStep[t-1],{y[0]==1}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \begin {array}{cc} \{ & \begin {array}{cc} e^t & t\leq 1 \\ -2+2 e^{t-1}+e^t & \text {True} \\ \end {array} \\ \end {array} \]