Coriolis Force

This is a problem in my class.mech textbook that I cannot solve, the midterm is coming up and the prof said to especially focus on these types of problems, so any help on what substitutions to make or any equation I'm forgetting about, would be fantastic, :P

The Question:
"Consider a particle that feels an angular force only, of the form F=2mvw(theta direction). Show that r=Ae^theta + Be^-theta, where A and B are constants of integration."
v=dr/dt
w=d(theta)/dt
I know to use separation of variables and then integrate, but I can't find a substitution that would make that possible.
also note that F=0 (radial direction) therefore: m((dv/dt)-r*w^2)=0 => dv/dt=r*w^2

Annnyy help would be appreciated :)

Awwww I was hoping to become super smart and answer with a scientific explanation of the Coriolis Effect on the oceans' currents (cause that's what I'm studying), but it's a physics problem :(

Yeah sorry about that, I couldn't think of a better name for the thread, "Physics problem" sounds sort of boring, and F=2mvw is known as the Coriolis Force
Thanks for wanting to help though haha