73.18.3 problem 27.1 (c)

Internal problem ID [15587]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 27. Differentiation and the Laplace transform. Additional Exercises. page 496
Problem number : 27.1 (c)
Date solved : Tuesday, January 28, 2025 at 08:02:52 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+3 y&=\operatorname {Heaviside}\left (t -4\right ) \end{align*}

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 10.723 (sec). Leaf size: 18

dsolve([diff(y(t),t)+3*y(t)=Heaviside(t-4),y(0) = 0],y(t), singsol=all)
 

\[ y = -\frac {\operatorname {Heaviside}\left (t -4\right ) \left (-1+{\mathrm e}^{-3 t +12}\right )}{3} \]

✓ Solution by Mathematica

Time used: 0.048 (sec). Leaf size: 27

DSolve[{D[y[t],t]+3*y[t]==UnitStep[t-4],{y[0]==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \begin {array}{cc} \{ & \begin {array}{cc} \frac {1}{3}-\frac {1}{3} e^{12-3 t} & t>4 \\ 0 & \text {True} \\ \end {array} \\ \end {array} \]