MATLAB: Best/fast approach to solve two coupled differential eigenvalue problem

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 2×2 matrices, the solution(eigenvector)u =(u1 u2)and E the eigenvalue

Best Answer

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.