27.2.3 problem 3

Internal problem ID [4303]
Book : An introduction to the solution and applications of differential equations, J.W. Searl, 1966
Section : Chapter 4, Ex. 4.2
Problem number : 3
Date solved : Monday, January 27, 2025 at 09:00:43 AM
CAS classification : [_separable]

\begin{align*} r y^{\prime }&=\frac {\left (a^{2}-r^{2}\right ) \tan \left (y\right )}{a^{2}+r^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.018 (sec). Leaf size: 17

dsolve(r*diff(y(r),r)= (a^2-r^2)/(a^2+r^2)*tan(y(r)),y(r), singsol=all)
 

\[ y \left (r \right ) = \arcsin \left (\frac {r c_{1}}{a^{2}+r^{2}}\right ) \]

✓ Solution by Mathematica

Time used: 23.758 (sec). Leaf size: 26

DSolve[r*D[y[r],r]== (a^2-r^2)/(a^2+r^2)*Tan[y[r]],y[r],r,IncludeSingularSolutions -> True]
 

\begin{align*} y(r)\to \arcsin \left (\frac {e^{c_1} r}{a^2+r^2}\right ) \\ y(r)\to 0 \\ \end{align*}