my question is: what is the general solution of this system of coupled diff. equations:

f ''i =Cijfj

Cij is a matrix, fj(z) are functions dependent of z. indexes i and j go from 0 to N .

- April 6th 2010, 06:26 AMqetuolSystem of second order linear homogenous differential coupled equations
my question is: what is the general solution of this system of coupled diff. equations:

f ''i =**C**ijfj

Cij is a matrix, fj(z) are functions dependent of z. indexes i and j go from 0 to N . - April 6th 2010, 06:48 AMshawsend
Hi. This is what I think it is without looking so I'm not sure ok? You have second-order DEs which I can convert to first-order DEs just by adding more variables. I'd then have a system of first-order autonomous DEs which I can then in principle, compute the eigenvalues and vectors and then claim, the solution is:

where is the set of eigenvalues and , the set of eigenvectors.

I don't know. Is that right guys? - April 7th 2010, 09:30 AMqetuol
sure i know linearization is a sulution. however i think there should be a general solution somewhere since it is "known" system , isnt it?

- April 12th 2010, 02:23 AMqetuol
okay, i found a possible solution:

where are integrating constants.. cj are eigenvalues of C and are complex..

if so, one question remains... how are the indexes assigned to eigenvalues? i mean which eigenvalue will be c1....?

is this correct? - April 23rd 2010, 08:11 AMqetuol
anyone can answer me ? please?