15.8.17 problem 17

Internal problem ID [3020]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 12, page 46
Problem number : 17
Date solved : Monday, January 27, 2025 at 07:08:58 AM
CAS classification : [_separable]

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

✓ Solution by Maple

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

dsolve(diff(r(theta),theta)=r(theta)*cot(theta),r(theta), singsol=all)
 

\[ r = c_{1} \sin \left (\theta \right ) \]

✓ Solution by Mathematica

Time used: 0.035 (sec). Leaf size: 15

DSolve[D[ r[\[Theta]], \[Theta] ]==r[\[Theta]]*Cot[\[Theta]],r[\[Theta]],\[Theta],IncludeSingularSolutions -> True]
 

\begin{align*} r(\theta )\to c_1 \sin (\theta ) \\ r(\theta )\to 0 \\ \end{align*}