52.6.13 problem 63

Internal problem ID [8348]
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 : 63
Date solved : Sunday, March 30, 2025 at 12:52:33 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+y&=\left \{\begin {array}{cc} 0 & 0\le t <1 \\ 5 & 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: 0.088 (sec). Leaf size: 22

ode:=diff(y(t),t)+y(t) = piecewise(0 <= t and t < 1,0,1 <= t,5); 
ic:=y(0) = 0; 
dsolve([ode,ic],y(t),method='laplace');
 

\[ y = \left \{\begin {array}{cc} 0 & t <1 \\ -5 \,{\mathrm e}^{1-t}+5 & 1\le t \end {array}\right . \]

✓ Mathematica. Time used: 0.047 (sec). Leaf size: 23

ode=D[y[t],t]+y[t]==Piecewise[{{0,0<=t<1},{5,t>=1}}]; 
ic={y[0]==0}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to \begin {array}{cc} \{ & \begin {array}{cc} 0 & t\leq 1 \\ 5-5 e^{1-t} & \text {True} \\ \end {array} \\ \end {array} \]

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-Piecewise((0, (t >= 0) & (t < 1)), (5, t >= 1)) + y(t) + Derivative(y(t), t),0) 
ics = {y(0): 0} 
dsolve(ode,func=y(t),ics=ics)