Internal problem ID [3991]
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]
Solve \begin {gather*} \boxed {r^{\prime }-\left (r+{\mathrm e}^{-\theta }\right ) \tan \left (\theta \right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 26
dsolve(diff(r(theta),theta)=(r(theta)+exp(-theta))*tan(theta),r(theta), singsol=all)
\[ r \left (\theta \right ) = \frac {c_{1}}{\cos \left (\theta \right )}-\frac {{\mathrm e}^{-\theta } \left (\sin \left (\theta \right )+\cos \left (\theta \right )\right )}{2 \cos \left (\theta \right )} \]
✓ Solution by Mathematica
Time used: 0.173 (sec). Leaf size: 24
DSolve[r'[\[Theta]]==(r[\[Theta]]+Exp[-\[Theta]])*Tan[\[Theta]],r[\[Theta]],\[Theta],IncludeSingularSolutions -> True]
\begin{align*} r(\theta )\to -\frac {1}{2} e^{-\theta } (\tan (\theta )+1)+c_1 \sec (\theta ) \\ \end{align*}