2.9 problem 9

Internal problem ID [4450]

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]

Solve \begin {gather*} \boxed {r^{\prime }+r \tan \left (\theta \right )-\sec \left (\theta \right )=0} \end {gather*}

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)
 

\[ r \left (\theta \right ) = \left (\tan \left (\theta \right )+c_{1}\right ) \cos \left (\theta \right ) \]

Solution by Mathematica

Time used: 0.083 (sec). Leaf size: 13

DSolve[r'[\[Theta]]+r[\[Theta]]*Tan[\[Theta]]==Sec[\[Theta]],r[\[Theta]],\[Theta],IncludeSingularSolutions -> True]
 

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