Internal problem ID [5915]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, class A]]
Solve \begin {gather*} \boxed {y^{\prime }+4 y-{\mathrm e}^{-4 t}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 12
dsolve([diff(y(t),t)+4*y(t)=exp(-4*t),y(0) = 2],y(t), singsol=all)
\[ y \relax (t ) = \left (2+t \right ) {\mathrm e}^{-4 t} \]
✓ Solution by Mathematica
Time used: 0.081 (sec). Leaf size: 14
DSolve[{y'[t]+4*y[t]==Exp[-4*t],{y[0]==2}},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to e^{-4 t} (t+2) \\ \end{align*}