36.2.9 problem 9

Internal problem ID [6302]
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
Date solved : Monday, January 27, 2025 at 01:55:30 PM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 11

dsolve(diff(r(theta),theta)+r(theta)*tan(theta)=sec(theta),r(theta), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.042 (sec). Leaf size: 13

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

\[ r(\theta )\to \sin (\theta )+c_1 \cos (\theta ) \]