BVP of two second order differential equations, with fitting point in the interval

Hi folks,

I have two second order differential equations:

1) y'' = ((A1+B1*x+C1*y)/D)^E * (1+y'^2)^3/2 on the interval 0<x<xc

and

2) y'' = ((A2+B2*x+C2*y)/D)^E * (1+y'^2)^3/2 on the interval xc<x<l

With following boundary conditions:

y'(0) = 0;

y(l) = 0;

y1(xc) = y2(xc);

y1'(xc) = y2'(xc);

Now I'm using bvp4c for solving each of them on interval 0<x<l, but I need to fit them in the middle of the interval e.g. point xc.

I cannot find a tutorial with this kind of task, can you help me with this problem? I believe this is not a very difficult problem, however I cannot find the solution.

Thank you in advance.