20.21.1 problem Problem 1

Internal problem ID [3928]
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 1
Date solved : Monday, January 27, 2025 at 08:04:39 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }-2 y&=6 \,{\mathrm e}^{5 t} \end{align*}

Using Laplace method With initial conditions

\begin{align*} y \left (0\right )&=3 \end{align*}

✓ Solution by Maple

Time used: 3.291 (sec). Leaf size: 15

dsolve([diff(y(t),t)-2*y(t)=6*exp(5*t),y(0) = 3],y(t), singsol=all)
 

\[ y = {\mathrm e}^{2 t}+2 \,{\mathrm e}^{5 t} \]

✓ Solution by Mathematica

Time used: 0.047 (sec). Leaf size: 18

DSolve[{D[y[t],t]-2*y[t]==6*Exp[5*t],{y[0]==3}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{2 t}+2 e^{5 t} \]