Internal problem ID [4499]
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 11.5, page 97.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {r^{\prime }-\left (r+{\mathrm e}^{-\theta }\right ) \tan \left (\theta \right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
dsolve(diff(r(theta),theta)=(r(theta)+exp(-theta))*tan(theta),r(theta), singsol=all)
\[ r \left (\theta \right ) = \frac {\left (-\tan \left (\theta \right )-1\right ) {\mathrm e}^{-\theta }}{2}+\sec \left (\theta \right ) c_{1} \]
✓ Solution by Mathematica
Time used: 0.093 (sec). Leaf size: 24
DSolve[r'[\[Theta]]==(r[\[Theta]]+Exp[-\[Theta]])*Tan[\[Theta]],r[\[Theta]],\[Theta],IncludeSingularSolutions -> True]
\[ r(\theta )\to -\frac {1}{2} e^{-\theta } (\tan (\theta )+1)+c_1 \sec (\theta ) \]