Numerical method to solve ODE boundary problem

[zetafunction]

can anyone provide a Numerical algorithm to solve

$$-y'' (x) +f(x)y(x) = \lambda _{n} y(x)$$

with the boundary condition $$y(0)=y(a)=0$$

here 'a' is a parameter introduced at hand inside the program

and $$f(x)$$ is also introduced by hand in the program

i am more interested in getting eingenvalues than obtaining Eigenfunctions

if possible the routine may be in MATHLAB or in FORTRAN thanks

another question can MATHEMATICA solve this kind of eigenvalue problems ??

 

[Charles49]

This is just a second order ordinary differential equation. Go here:
http://mathworld.wolfram.com/Second-OrderOrdinaryDifferentialEquation.html
The eigenvalues are simply the zeros of $$-z^2+z\left(f(z)-\lambda_n\right)=0$$. Go here:
http://www.sosmath.com/diffeq/second/euler/euler.html

You can use the Newton's method to find the zeros.