System of ODE for functions with different origins

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SUMMARY

The discussion centers on solving a system of coupled ordinary differential equations (ODEs) with shifted origins for the functions Y1 and Y2. The equations presented are: a1 * Y1" + a2 * Y2" + b1 * Y1 + b2 * Y2 = 0 and a2 * Y1" + a3 * Y2" + b2 * Y1 + b3 * Y2 = 0. The suggested approach is to first solve the system without considering the shifts in origins and then apply a translation to account for the shifts in the coordinates of Y1 and Y2. This method effectively simplifies the problem before addressing the complexities introduced by the shifts.

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

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