35.8.23 problem 23

Internal problem ID [6230]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 13. Miscellaneous problems. page 466
Problem number : 23
Date solved : Monday, January 27, 2025 at 01:49:29 PM
CAS classification : [_linear]

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

✓ Solution by Maple

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

dsolve(sin(theta)*cos(theta)*diff(r(theta),theta)-sin(theta)^2=r(theta)*cos(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: 0.039 (sec). Leaf size: 14

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

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