52.6.1 problem 21

Internal problem ID [8336]
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
Date solved : Monday, January 27, 2025 at 03:49:11 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+4 y&={\mathrm e}^{-4 t} \end{align*}

Using Laplace method With initial conditions

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

✓ Solution by Maple

Time used: 0.553 (sec). Leaf size: 12

dsolve([diff(y(t),t)+4*y(t)=exp(-4*t),y(0) = 2],y(t), singsol=all)
 

\[ y = \left (t +2\right ) {\mathrm e}^{-4 t} \]

✓ Solution by Mathematica

Time used: 0.065 (sec). Leaf size: 14

DSolve[{D[y[t],t]+4*y[t]==Exp[-4*t],{y[0]==2}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-4 t} (t+2) \]