Internal problem ID [4958]
Book: Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston.
Pearson 2018.
Section: Chapter 2, First order differential equations. Section 2.3, Linear equations. Exercises.
page 54
Problem number: 9.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {r^{\prime }+\tan \left (\theta \right ) r=\sec \left (\theta \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 11
dsolve(diff(r(theta),theta)+r(theta)*tan(theta)=sec(theta),r(theta), singsol=all)
\[ r \left (\theta \right ) = \cos \left (\theta \right ) c_{1} +\sin \left (\theta \right ) \]
✓ Solution by Mathematica
Time used: 0.048 (sec). Leaf size: 13
DSolve[r'[\[Theta]]+r[\[Theta]]*Tan[\[Theta]]==Sec[\[Theta]],r[\[Theta]],\[Theta],IncludeSingularSolutions -> True]
\[ r(\theta )\to \sin (\theta )+c_1 \cos (\theta ) \]