83.2.7 problem 2 (b)

Internal problem ID [21918]
Book : Differential Equations By Kaj L. Nielsen. Second edition 1966. Barnes and nobel. 66-28306
Section : Chapter III. First order differential equations of the first degree. Ex. III at page 35
Problem number : 2 (b)
Date solved : Thursday, October 02, 2025 at 08:09:37 PM
CAS classification : [_separable]

\begin{align*} r^{\prime }&=r \tan \left (t \right ) \end{align*}

With initial conditions

\begin{align*} r \left (0\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 6

ode:=diff(r(t),t) = r(t)*tan(t); 
ic:=[r(0) = 1]; 
dsolve([ode,op(ic)],r(t), singsol=all);
 

\[ r = \sec \left (t \right ) \]

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 7

ode=D[r[t],t]==r[t]*Tan[t]; 
ic={r[0]==1}; 
DSolve[{ode,ic},r[t],t,IncludeSingularSolutions->True]
 

\begin{align*} r(t)&\to \sec (t) \end{align*}

✓ Sympy. Time used: 0.127 (sec). Leaf size: 7

from sympy import * 
t = symbols("t") 
r = Function("r") 
ode = Eq(-r(t)*tan(t) + Derivative(r(t), t),0) 
ics = {r(0): 1} 
dsolve(ode,func=r(t),ics=ics)
 

\[ r{\left (t \right )} = \frac {1}{\cos {\left (t \right )}} \]