Internal problem ID [2633]
Book: An introduction to the solution and applications of differential equations, J.W. Searl,
1966
Section: Chapter 4, Ex. 4.2
Problem number: 3.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {r y^{\prime }-\frac {\left (a^{2}-r^{2}\right ) \tan \relax (y)}{a^{2}+r^{2}}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.007 (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)
\[ y \relax (r ) = \arcsin \left (\frac {r c_{1}}{a^{2}+r^{2}}\right ) \]
✓ Solution by Mathematica
Time used: 4.065 (sec). Leaf size: 26
DSolve[r*y'[r]== (a^2-r^2)/(a^2+r^2)*Tan[y[r]],y[r],r,IncludeSingularSolutions -> True]
\begin{align*} y(r)\to \text {ArcSin}\left (\frac {e^{c_1} r}{a^2+r^2}\right ) \\ y(r)\to 0 \\ \end{align*}