83.2.4 problem 1 (d)

Internal problem ID [21915]
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 : 1 (d)
Date solved : Thursday, October 02, 2025 at 08:09:31 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.000 (sec). Leaf size: 8

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

\[ r = c_1 \csc \left (t \right ) \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 15

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

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

✓ Sympy. Time used: 0.142 (sec). Leaf size: 7

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

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