86.9.9 problem 17

Internal problem ID [23179]
Book : An introduction to Differential Equations. By Howard Frederick Cleaves. 1969. Oliver and Boyd publisher. ISBN 0050015044
Section : Chapter 7. Polar coordinates and vectors. Exercise 7a at page 109
Problem number : 17
Date solved : Thursday, October 02, 2025 at 09:24:00 PM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} r \left (0\right )&=a \\ \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 9

ode:=diff(r(theta),theta) = c; 
ic:=[r(0) = a]; 
dsolve([ode,op(ic)],r(theta), singsol=all);
 

\[ r = c \theta +a \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 10

ode=D[r[\[Theta]],\[Theta]]==c; 
ic={r[0]==a}; 
DSolve[{ode,ic},r[\[Theta]],\[Theta],IncludeSingularSolutions->True]
 

\begin{align*} r(\theta )&\to a+c \theta \end{align*}

✓ Sympy. Time used: 0.023 (sec). Leaf size: 7

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

\[ r{\left (t \right )} = a + c t \]