Internal problem ID [3995]
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]
Solve \begin {gather*} \boxed {\tan \left (\theta \right ) r^{\prime }-r-\left (\tan ^{2}\left (\theta \right )\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (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: 0.059 (sec). Leaf size: 43
DSolve[Tan[\[Theta]]*r'[\[Theta]]-r[\[Theta]]==Tan[\[Theta]]^2,r[\[Theta]],\[Theta],IncludeSingularSolutions -> True]
\begin{align*} r(\theta )\to \sin (\theta ) \left (-\log \left (\cos \left (\frac {\theta }{2}\right )-\sin \left (\frac {\theta }{2}\right )\right )+\log \left (\sin \left (\frac {\theta }{2}\right )+\cos \left (\frac {\theta }{2}\right )\right )+c_1\right ) \\ \end{align*}