Internal problem ID [4484]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {\cos \left (\theta \right ) r^{\prime }-r \sin \left (\theta \right )+{\mathrm e}^{\theta }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve(cos(theta)*diff(r(theta),theta)-(r(theta)*sin(theta)-exp(theta))=0,r(theta), singsol=all)
\[ r \left (\theta \right ) = \frac {-{\mathrm e}^{\theta }+c_{1}}{\cos \left (\theta \right )} \]
✓ Solution by Mathematica
Time used: 0.094 (sec). Leaf size: 16
DSolve[Cos[\[Theta]]*r'[\[Theta]]-(r[\[Theta]]*Sin[\[Theta]]-Exp[\[Theta]])==0,r[\[Theta]],\[Theta],IncludeSingularSolutions -> True]
\begin{align*} r(\theta )\to \left (-e^{\theta }+c_1\right ) \sec (\theta ) \\ \end{align*}