Math Is Fun Forum

Identity

Member

Registered: 2007-04-18

Posts: 934

Solving systems of DEs

I'm familiar with how to solve systems of DEs of the form

where

and

is a constant matrix, but how do you solve DEs of the form

where

is a constant translation?

Thanks

matthen

Member

Registered: 2011-03-06

Posts: 8

Re: Solving systems of DEs

If you did a change of variables

then

remains unchanged.
You know how to solve

(eigenvectors right?)
so what would that change of variables have to be to put the equation in this form?

So we only need:

So if

is invertible, let:

Then you can solve

and then go back to the original variables by sending:

Last edited by matthen (2011-03-07 00:05:58)

Identity

Member

Registered: 2007-04-18

Posts: 934

Re: Solving systems of DEs

Thanks matthen! That's pretty clever

Last edited by Identity (2011-03-07 00:19:43)

matthen

Member

Registered: 2011-03-06

Posts: 8

Re: Solving systems of DEs

No worries