Internal problem ID [2332]
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 3.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, class A]]
Solve \begin {gather*} \boxed {y^{\prime }+3 y-2 \,{\mathrm e}^{-t}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 3] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 15
dsolve([diff(y(t),t)+3*y(t)=2*exp(-t),y(0) = 3],y(t), singsol=all)
\[ y \relax (t ) = \left ({\mathrm e}^{2 t}+2\right ) {\mathrm e}^{-3 t} \]
✓ Solution by Mathematica
Time used: 0.058 (sec). Leaf size: 18
DSolve[{y'[t]+3*y[t]==2*Exp[-t],{y[0]==3}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to e^{-3 t} \left (e^{2 t}+2\right ) \\ \end{align*}