38.6.55 problem 60

Internal problem ID [8485]
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, September 30, 2025 at 05:38:04 PM
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*}

✓ Maple. Time used: 0.032 (sec). Leaf size: 19

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

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

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 21

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

\begin{align*} e(t)&\to \text {e0} e^{\frac {4-t}{c r}} \end{align*}

✓ Sympy. Time used: 0.074 (sec). Leaf size: 17

from sympy import * 
t = symbols("t") 
c = symbols("c") 
r = symbols("r") 
e = Function("e") 
ode = Eq(Derivative(e(t), t) + e(t)/(c*r),0) 
ics = {e(4): e__0} 
dsolve(ode,func=e(t),ics=ics)
 

\[ e{\left (t \right )} = e^{0} e^{\frac {4}{c r}} e^{- \frac {t}{c r}} \]