Internal problem ID [3994]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 11, Bernoulli
Equations
Problem number: Exercise 11.9, page 97.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {\tan \left (\theta \right ) r^{\prime }-r-\tan \left (\theta \right )^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve(tan(theta)*diff(r(theta),theta)-r(theta)=tan(theta)^2,r(theta), singsol=all)
\[ r \left (\theta \right ) = \left (\ln \left (\sec \left (\theta \right )+\tan \left (\theta \right )\right )+c_{1} \right ) \sin \left (\theta \right ) \]
✓ Solution by Mathematica
Time used: 0.05 (sec). Leaf size: 14
DSolve[Tan[\[Theta]]*r'[\[Theta]]-r[\[Theta]]==Tan[\[Theta]]^2,r[\[Theta]],\[Theta],IncludeSingularSolutions -> True]
\begin{align*} r(\theta )\to \sin (\theta ) (\text {arctanh}(\sin (\theta ))+c_1) \\ \end{align*}