Internal problem ID [2049]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {r^{\prime }-r \cot \left (\theta \right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 8
dsolve(diff(r(theta),theta)=r(theta)*cot(theta),r(theta), singsol=all)
\[ r \left (\theta \right ) = c_{1} \sin \left (\theta \right ) \]
✓ Solution by Mathematica
Time used: 0.038 (sec). Leaf size: 15
DSolve[r'[\[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*}