How can I solve an ODE when F(x0)=F'(x0)=0 is given at an unknown point x=x0 using bvp5c?

Hi, I'm attempting to solve the following ODE using bvp5c. I've used bvp5c for other typical multipoint boundary value problems but I have no idea how to deal with ODEs with conditions given at an unknown point x0.

(x-C)+1/2*Sigma^2*x^2*F''(x) + r*x*F'(x) - r*F(x) = 0 where F(x0) = F'(x0) = 0, x0 is unknown.

I guess I should make use of the parameter in bvp5c (to solve for f(x) and x0 together). Can anyone help me? Thanks in advance.

Answer 1

[Bill Greene]

You have a second order ODE so you need two boundary conditions. The term "boundary condition" implies that you know the location(s) where they are prescribed. Your problem description has no criterion for determining x0 so the problem is ill-posed (i.e. doesn't have a solution).