44.6.55 problem 60

Internal problem ID [7199]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 2. First order differential equations. Section 2.3 Linear equations. Exercises 2.3 at page 63
Problem number : 60
Date solved : Tuesday, February 04, 2025 at 12:47:18 AM
CAS classification : [_quadrature]

\begin{align*} e^{\prime }&=-\frac {e}{r c} \end{align*}

With initial conditions

\begin{align*} e \left (4\right )&=e_{0} \end{align*}

✓ Solution by Maple

Time used: 0.021 (sec). Leaf size: 19

dsolve([diff(e(t),t)=-1/(r*c)*e(t),e(4) = e__0],e(t), singsol=all)
 

\[ e = e_{0} {\mathrm e}^{\frac {-t +4}{r c}} \]

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 21

DSolve[{D[e[t],t]==-1/(r*c)*e[t],{e[4]==e0}},e[t],t,IncludeSingularSolutions -> True]
 

\[ e(t)\to \text {e0} e^{\frac {4-t}{c r}} \]