Using ode45 vs bvp4/5c to solve a simple wave equation

I need to solve some exotic forms of Schrodinger's Equation in MATLAB in order to find the eigenvalues of the system. My issue is that typically only the boundary values of the system are known (the solution should decay to 0 at the boundaries), and not the initial values. So, I am looking to use bvp4/5c instead of ode45 (with which I am much more familiar). However, I am running into bizarre issues with bvp4/5c, even with just the simple y''+y=0 equation.

Messing with the domain of integration often causes insane rescaling of the solution (sometimes of order e-10 to e+10), and solutions just don't look very nice if I instead choose y''+5y=0. I suspect both of these issues have to do with the quality of my "guessed" solution, but this idea of guessing a solution works terribly for exotic, nonlinear potentials.

Any ideas on how to handle this?

Thanks.