Internal problem ID [11618]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 2, section 2.2 (Separable equations). Exercises page 47
Problem number: 5.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\tan \left (\theta \right )+2 r \theta ^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.313 (sec). Leaf size: 21
dsolve(tan(theta(r))+2*r*diff(theta(r),r)=0,theta(r), singsol=all)
\begin{align*} \theta \left (r \right ) &= \arcsin \left (\frac {1}{\sqrt {c_{1} r}}\right ) \\ \theta \left (r \right ) &= -\arcsin \left (\frac {1}{\sqrt {c_{1} r}}\right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 15.319 (sec). Leaf size: 21
DSolve[Tan[theta[r]]+2*r*theta'[r]==0,theta[r],r,IncludeSingularSolutions -> True]
\begin{align*} \theta (r)\to \arcsin \left (\frac {e^{c_1}}{\sqrt {r}}\right ) \\ \theta (r)\to 0 \\ \end{align*}