20.23.4 problem Problem 4

Internal problem ID [3976]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 10, The Laplace Transform and Some Elementary Applications. Exercises for 10.8. page 710
Problem number : Problem 4
Date solved : Sunday, March 30, 2025 at 02:13:30 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }-5 y&=2 \,{\mathrm e}^{-t}+\delta \left (t -3\right ) \end{align*}

Using Laplace method With initial conditions

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

✓ Maple. Time used: 0.136 (sec). Leaf size: 28

ode:=diff(y(t),t)-5*y(t) = 2*exp(-t)+Dirac(t-3); 
ic:=y(0) = 0; 
dsolve([ode,ic],y(t),method='laplace');
 

\[ y = {\mathrm e}^{5 t -15} \operatorname {Heaviside}\left (t -3\right )-\frac {{\mathrm e}^{-t}}{3}+\frac {{\mathrm e}^{5 t}}{3} \]

✓ Mathematica. Time used: 0.098 (sec). Leaf size: 34

ode=D[y[t],t]-5*y[t]==2*Exp[-t]+DiracDelta[t-3]; 
ic={y[0]==0}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to \frac {1}{3} e^{-t} \left (3 e^{6 t-15} \theta (t-3)+e^{6 t}-1\right ) \]

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-Dirac(t - 3) - 5*y(t) + Derivative(y(t), t) - 2*exp(-t),0) 
ics = {y(0): 0} 
dsolve(ode,func=y(t),ics=ics)
 

Timed Out