20.22.2 problem Problem 28

Internal problem ID [3957]
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 28
Date solved : Monday, January 27, 2025 at 08:04:59 AM
CAS classification : [[_linear, `class A`]]

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

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 3.510 (sec). Leaf size: 32

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

\[ y = -\operatorname {Heaviside}\left (t -2\right ) {\mathrm e}^{t -2}+\operatorname {Heaviside}\left (t -2\right ) {\mathrm e}^{2 t -4}+2 \,{\mathrm e}^{2 t} \]

✓ Solution by Mathematica

Time used: 0.097 (sec). Leaf size: 40

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

\[ y(t)\to \begin {array}{cc} \{ & \begin {array}{cc} 2 e^{2 t} & t\leq 2 \\ e^{t-4} \left (-e^2+e^t+2 e^{t+4}\right ) & \text {True} \\ \end {array} \\ \end {array} \]