Best/fast approach to solve two coupled differential eigenvalue problem

Which method in matlab is the best/fastest way to solve the eigenvalue problem of following system of differetial equations (two coupled differential equations, in this case only in one dimension):

(Md2/dr2 + W ) u = E u, where d2/dr2 is in one dimension, M and W are 2x2 matrices, the solution(eigenvector)u =(u1 u2)and E the eigenvalue

Answer 1

[Torsten]

Maybe the example

"Compute Fourth Eigenvalue of Mathieu's Equation"

under

https://de.mathworks.com/help/matlab/ref/bvp4c.html

is of help.

Best wishes

Torsten.