Internal problem ID [12434]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {r^{\prime }+r \tan \left (t \right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 8
dsolve(diff(r(t),t)+r(t)*tan(t)=0,r(t), singsol=all)
\[ r \left (t \right ) = \cos \left (t \right ) c_{1} \]
✓ Solution by Mathematica
Time used: 0.068 (sec). Leaf size: 15
DSolve[r'[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*}