BVP for system of 2 second order ODEs

I have a system of two second order ODEs that I want to calculate using bvp4c. I have some problems transforming the second order ODEs in acceptable first order problems and then setting up the boundary conditions. Help is very much appreciated!

My system of equations with and :

where , , , and h are known constant values and is a known linear function.

The boundary conditions are:

,

,

,

I have some problems setting this up, because and are appearing in both ODEs.

Thanks in advance!

Answer 1

[Alan Stevens]

Here is how you can express your second order equations as first order ones

You should now be able to express your boundary conditions ok, though you seem to have too many! You have four initial conditions which should be enough to determine your dependent variables.