This is a boundary value problem, not a initial value problem. Actually, function u2a[x] is defined on 1/2=<x<=1, and u6b[x] is defined on 1=<x<=3/2, so there cannot be u2a'[0] and u6b[0]. I don't think there is anything wrong with my boundary conditions, since I wrote them according to the basic principles of mechanics, although I could not guarantee that they are 100% correct. Anyway, many thanks for your reply and help!
