Question

(Sturm-Liouville)(ODE) I'm still having trouble understanding how to solve a certain ODE and obtain the result in the following worked problem (link/info below):

Answer 1

I don't understand how, on page 12 for example 5.2.5.1, they are getting sinh(x) and cosh(x) for the general solution when lambda is equal to negative omega squared.

http://texas.math.ttu.edu/~gilliam/ttu/ode_pde_pdf/Ch5.pdf

Answer 2

@dan815

Answer 3

Lambda being positive omega squared makes sense to me, so does it being zero, but I don't understand how they get their results when it's negative omega squared.

Answer 4

Nevermind, I think I figured it out: I believe it has to do with this. http://tutorial.math.lamar.edu/Classes/DE/BVPEvals.aspx