38.5.15 problem 15

Internal problem ID [8363]
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 2.2 Separable equations. Exercises 2.2 at page 53
Problem number : 15
Date solved : Tuesday, September 30, 2025 at 05:30:08 PM
CAS classification : [_quadrature]

\begin{align*} s^{\prime }&=k s \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 10

ode:=diff(s(r),r) = k*s(r); 
dsolve(ode,s(r), singsol=all);
 

\[ s = c_1 \,{\mathrm e}^{k r} \]

✓ Mathematica. Time used: 0.015 (sec). Leaf size: 18

ode=D[s[r],r]==k*s[r]; 
ic={}; 
DSolve[{ode,ic},s[r],r,IncludeSingularSolutions->True]
 

\begin{align*} s(r)&\to c_1 e^{k r}\\ s(r)&\to 0 \end{align*}

✓ Sympy. Time used: 0.060 (sec). Leaf size: 8

from sympy import * 
r = symbols("r") 
k = symbols("k") 
s = Function("s") 
ode = Eq(-k*s(r) + Derivative(s(r), r),0) 
ics = {} 
dsolve(ode,func=s(r),ics=ics)
 

\[ s{\left (r \right )} = C_{1} e^{k r} \]