73.21.1 problem 30.6 (a)

Internal problem ID [15620]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 30. Piecewise-defined functions and periodic functions. Additional Exercises. page 553
Problem number : 30.6 (a)
Date solved : Tuesday, January 28, 2025 at 08:03:14 AM
CAS classification : [_quadrature]

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

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 9.109 (sec). Leaf size: 12

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

\[ y = \operatorname {Heaviside}\left (t -3\right ) \left (t -3\right ) \]

✓ Solution by Mathematica

Time used: 0.006 (sec). Leaf size: 15

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

\[ y(t)\to \begin {array}{cc} \{ & \begin {array}{cc} t-3 & t>3 \\ 0 & \text {True} \\ \end {array} \\ \end {array} \]