20.21.2 problem Problem 2

Internal problem ID [3929]
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 10.4. page 689
Problem number : Problem 2
Date solved : Tuesday, March 04, 2025 at 05:19:37 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+y&=8 \,{\mathrm e}^{3 t} \end{align*}

Using Laplace method With initial conditions

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

✓ Maple. Time used: 2.523 (sec). Leaf size: 10

ode:=diff(y(t),t)+y(t) = 8*exp(3*t); 
ic:=y(0) = 2; 
dsolve([ode,ic],y(t),method='laplace');
 

\[ y = 2 \,{\mathrm e}^{3 t} \]

✓ Mathematica. Time used: 0.047 (sec). Leaf size: 12

ode=D[y[t],t]+y[t]==8*Exp[3*t]; 
ic={y[0]==2}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to 2 e^{3 t} \]

✓ Sympy. Time used: 0.139 (sec). Leaf size: 8

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(y(t) - 8*exp(3*t) + Derivative(y(t), t),0) 
ics = {y(0): 2} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = 2 e^{3 t} \]