52.6.14 problem 64

Internal problem ID [8349]
Book : DIFFERENTIAL EQUATIONS with Boundary Value Problems. DENNIS G. ZILL, WARREN S. WRIGHT, MICHAEL R. CULLEN. Brooks/Cole. Boston, MA. 2013. 8th edition.
Section : CHAPTER 7 THE LAPLACE TRANSFORM. 7.3.1 TRANSLATION ON THE s-AXIS. Page 297
Problem number : 64
Date solved : Sunday, March 30, 2025 at 12:52:34 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+y&=\left \{\begin {array}{cc} 1 & 0\le t <1 \\ -1 & 1\le t \end {array}\right . \end{align*}

Using Laplace method With initial conditions

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

✓ Maple. Time used: 0.133 (sec). Leaf size: 31

ode:=diff(y(t),t)+y(t) = piecewise(0 <= t and t < 1,1,1 <= t,-1); 
ic:=y(0) = 0; 
dsolve([ode,ic],y(t),method='laplace');
 

\[ y = -{\mathrm e}^{-t}-\left (\left \{\begin {array}{cc} -1 & t <1 \\ 1-2 \,{\mathrm e}^{1-t} & 1\le t \end {array}\right .\right ) \]

✓ Mathematica. Time used: 0.069 (sec). Leaf size: 43

ode=D[y[t],t]+y[t]==Piecewise[{{1,0<=t<1},{-1,t>=1}}]; 
ic={y[0]==0}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

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

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-Piecewise((1, (t >= 0) & (t < 1)), (-1, t >= 1)) + y(t) + Derivative(y(t), t),0) 
ics = {y(0): 0} 
dsolve(ode,func=y(t),ics=ics)