I have to show that the solution of a differential equation is an arc of...
I have to show that the solution of a differential equation is an arc of a great circle. The differential equation is as follows (in spherical coordinates):
where is an arbitrary constant and denotes the derivative of with respect to .
By setting , any arc of a great circle will have no change in with respect to , so with this initial condition the answer follows by proving that . My issue is that upon working this round I end up with
From this I can see no way forward.
Where do i go from here/ what should I do instead?