67.21.1 problem 30.6 (a)

Internal problem ID [16907]
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 : Thursday, October 02, 2025 at 01:40:16 PM
CAS classification : [_quadrature]

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

Using Laplace method With initial conditions

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

✓ Maple. Time used: 0.106 (sec). Leaf size: 12

ode:=diff(y(t),t) = Heaviside(t-3); 
ic:=[y(0) = 0]; 
dsolve([ode,op(ic)],y(t),method='laplace');
 

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

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 15

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

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

✓ Sympy. Time used: 0.175 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-Heaviside(t - 3) + Derivative(y(t), t),0) 
ics = {y(0): 0} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \begin {cases} 0 & \text {for}\: \left |{t}\right | < 3 \\t {G_{2, 2}^{0, 2}\left (\begin {matrix} 0, 1 & \\ & -1, 0 \end {matrix} \middle | {\frac {t}{3}} \right )} & \text {otherwise} \end {cases} \]