32.5.9 problem Exercise 11.9, page 97

Internal problem ID [5847]
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
Date solved : Monday, January 27, 2025 at 01:20:38 PM
CAS classification : [_linear]

\begin{align*} \tan \left (\theta \right ) r^{\prime }-r&=\tan \left (\theta \right )^{2} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 15

dsolve(tan(theta)*diff(r(theta),theta)-r(theta)=tan(theta)^2,r(theta), singsol=all)
 

\[ r = \left (\ln \left (\sec \left (\theta \right )+\tan \left (\theta \right )\right )+c_{1} \right ) \sin \left (\theta \right ) \]

✓ Solution by Mathematica

Time used: 0.053 (sec). Leaf size: 14

DSolve[Tan[\[Theta]]*D[ r[\[Theta]], \[Theta] ]-r[\[Theta]]==Tan[\[Theta]]^2,r[\[Theta]],\[Theta],IncludeSingularSolutions -> True]
 

\[ r(\theta )\to \sin (\theta ) \left (\coth ^{-1}(\sin (\theta ))+c_1\right ) \]