69.1.17 problem 17

Internal problem ID [14170]
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 : Tuesday, January 28, 2025 at 06:18:38 AM
CAS classification : [_separable]

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

✓ Solution by Maple

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

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

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

✓ Solution by Mathematica

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

DSolve[D[r[t],t]+r[t]*Tan[t]==0,r[t],t,IncludeSingularSolutions -> True]
 

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