63.15.10 problem 6(j)

Internal problem ID [13193]
Book : A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY. 2015.
Section : Chapter 3, Laplace transform. Section 3.2.1 Initial value problems. Exercises page 156
Problem number : 6(j)
Date solved : Tuesday, January 28, 2025 at 05:12:12 AM
CAS classification : [[_linear, `class A`]]

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

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 8.988 (sec). Leaf size: 18

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

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

✓ Solution by Mathematica

Time used: 0.046 (sec). Leaf size: 25

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

\[ x(t)\to \begin {array}{cc} \{ & \begin {array}{cc} \frac {1}{2} \left (-1+e^{2 t-2}\right ) & t>1 \\ 0 & \text {True} \\ \end {array} \\ \end {array} \]