86.9.8 problem 16

Internal problem ID [23178]
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 : 16
Date solved : Thursday, October 02, 2025 at 09:23:59 PM
CAS classification : [_quadrature]

\begin{align*} r^{\prime }&=0 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 5

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

\[ r = 0 \]

✓ Mathematica. Time used: 0.001 (sec). Leaf size: 6

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

\begin{align*} r(\theta )&\to 0 \end{align*}

✓ Sympy. Time used: 0.014 (sec). Leaf size: 3

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

\[ r{\left (t \right )} = 0 \]