52.6.1 problem 21

Internal problem ID [8336]
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 : 21
Date solved : Wednesday, March 05, 2025 at 05:35:24 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+4 y&={\mathrm e}^{-4 t} \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=2 \end{align*}

✓ Maple. Time used: 0.553 (sec). Leaf size: 12

ode:=diff(y(t),t)+4*y(t) = exp(-4*t); 
ic:=y(0) = 2; 
dsolve([ode,ic],y(t),method='laplace');
 

\[ y = \left (t +2\right ) {\mathrm e}^{-4 t} \]

✓ Mathematica. Time used: 0.065 (sec). Leaf size: 14

ode=D[y[t],t]+4*y[t]==Exp[-4*t]; 
ic={y[0]==2}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to e^{-4 t} (t+2) \]

✓ Sympy. Time used: 0.156 (sec). Leaf size: 10

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(4*y(t) + Derivative(y(t), t) - exp(-4*t),0) 
ics = {y(0): 2} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \left (t + 2\right ) e^{- 4 t} \]