System of ODE for functions with different origins

[FrankST]

Hi,

I have a system of coupled ODE like:

a1 * Y1" + a2 * Y2" + b1 * Y1 + b2 * Y2 = 0
a2 * Y1" + a3 * Y2" + b2 * Y1 + b3 * Y2 = 0

I know for example by eigenvalue method I can solve it, but here is the issue: Y1 = f1 (x - a) and Y2 = f2 ( x - b). In the other word there is a shift between the coordinates that Y1 and Y2 are evaluated in. Now, I am wondering if you have any idea how I can solve this system of ODE.


Thanks a lot,

 

[Petr Mugver]

If the problem is the shift in the origins, first solve with the origins unshifted and at the end make a translation.