Internal problem ID [4377]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {\sin \left (\theta \right ) \cos \left (\theta \right ) r^{\prime }-\sin \left (\theta \right )^{2}-r \cos \left (\theta \right )^{2}=0} \]
✓ Solution by Maple
Time used: 0.016 (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)
\[ r \left (\theta \right ) = \left (\ln \left (\sec \left (\theta \right )+\tan \left (\theta \right )\right )+c_{1} \right ) \sin \left (\theta \right ) \]
✓ Solution by Mathematica
Time used: 0.041 (sec). Leaf size: 14
DSolve[Sin[\[Theta]]*Cos[\[Theta]]*r'[\[Theta]]-Sin[\[Theta]]^2==r[\[Theta]]*Cos[\[Theta]]^2,r[\[Theta]],\[Theta],IncludeSingularSolutions -> True]
\begin{align*} r(\theta )\to \sin (\theta ) (\text {arctanh}(\sin (\theta ))+c_1) \\ \end{align*}