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 : Monday, January 27, 2025 at 08:04:40 AM
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*}

✓ Solution by Maple

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

dsolve([diff(y(t),t)+y(t)=8*exp(3*t),y(0) = 2],y(t), singsol=all)
 

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

✓ Solution by Mathematica

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

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

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