36.3.14 problem 15

Internal problem ID [6335]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.4, Exact equations. Exercises. page 64
Problem number : 15
Date solved : Monday, January 27, 2025 at 01:56:52 PM
CAS classification : [_linear]

\begin{align*} \cos \left (\theta \right ) r^{\prime }-r \sin \left (\theta \right )+{\mathrm e}^{\theta }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 13

dsolve(cos(theta)*diff(r(theta),theta)-(r(theta)*sin(theta)-exp(theta))=0,r(theta), singsol=all)
 

\[ r = \left (-{\mathrm e}^{\theta }+c_1 \right ) \sec \left (\theta \right ) \]

✓ Solution by Mathematica

Time used: 0.052 (sec). Leaf size: 16

DSolve[Cos[\[Theta]]*D[ r[\[Theta]], \[Theta] ]-(r[\[Theta]]*Sin[\[Theta]]-Exp[\[Theta]])==0,r[\[Theta]],\[Theta],IncludeSingularSolutions -> True]
 

\[ r(\theta )\to \left (-e^{\theta }+c_1\right ) \sec (\theta ) \]