Internal problem ID [2002]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 10, page 41
Problem number: 16.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {\cos \left (\theta \right ) r^{\prime }-2 r \sin \left (\theta \right )=2} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
dsolve(cos(theta)*diff(r(theta),theta)=2+2*r(theta)*sin(theta),r(theta), singsol=all)
\[ r \left (\theta \right ) = \frac {4 \sin \left (\theta \right )+2 c_{1}}{\cos \left (2 \theta \right )+1} \]
✓ Solution by Mathematica
Time used: 0.052 (sec). Leaf size: 17
DSolve[Cos[\[Theta]]*r'[\[Theta]]==2+2*r[\[Theta]]*Sin[\[Theta]],r[\[Theta]],\[Theta],IncludeSingularSolutions -> True]
\[ r(\theta )\to \sec ^2(\theta ) (2 \sin (\theta )+c_1) \]