69.1.17 problem 17

Internal problem ID [14091]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 17
Date solved : Wednesday, March 05, 2025 at 10:31:00 PM
CAS classification : [_separable]

\begin{align*} r^{\prime }+r \tan \left (t \right )&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 8

ode:=diff(r(t),t)+r(t)*tan(t) = 0; 
dsolve(ode,r(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.037 (sec). Leaf size: 15

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

\begin{align*} r(t)\to c_1 \cos (t) \\ r(t)\to 0 \\ \end{align*}

✓ Sympy. Time used: 0.205 (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 = {} 
dsolve(ode,func=r(t),ics=ics)
 

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