64.4.5 problem 5

Internal problem ID [13294]
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
Date solved : Tuesday, January 28, 2025 at 05:16:16 AM
CAS classification : [_separable]

\begin{align*} \tan \left (\theta \right )+2 r \theta ^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.900 (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: 8.246 (sec). Leaf size: 21

DSolve[Tan[theta[r]]+2*r*D[ theta[r],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*}