Hello Everyone,

Now I am familiar, roughly, in solving systems of DEs with constant coefficients, granted that these equations are homogenous, but how can we solve such a system of equations:

Thanks a lot!

- Feb 27th 2011, 07:01 AMrebghbSystem of Linear Differential Equations with Constant Coefficients
Hello Everyone,

Now I am familiar, roughly, in solving systems of DEs with constant coefficients, granted that these equations are homogenous, but how can we solve such a system of equations:

Thanks a lot! - Feb 27th 2011, 07:12 AMFernandoRevilla
You have to find a particular solution of the complete system and add all the solutions of the homogeneous. There is a well known theorem about it. Have you studied the corresponding theory?

- Feb 27th 2011, 07:25 AMrebghb
I am afraid not, I konly know how to solve linear ODEs (not necessarily homogenous) and homogenous systems. I tried searching for an answer but didn't know what to search for.

- Feb 27th 2011, 11:18 AMFernandoRevilla
- Feb 27th 2011, 12:11 PMHallsofIvy
Well, no, the second equaton is NOT homogeneous.

Here is a much more elementary method:

Differentiate both sides of the first equation to get

From the second equation, so we can write that as

and now, from the first equation again, so we have

a single, non-homogeneous second order linear equation with constant coefficients. Once you have solved for you can use to find = - Feb 28th 2011, 02:45 AMrebghb
Thank you, I thought of that, honestly, but what I was looking for was something to solve a bigger problem, say 10 equations!

As I have posted earlier, we need to find the eigenvalues for the matrix, a step towards solving the system, shall the system be homogenous; but what if it isn't? Is there a particular procedure? If yes I'd like to know it's name, I'll try to search for it and learn it on my own... - Feb 28th 2011, 03:00 AMAckbeet
- Feb 28th 2011, 04:29 AMFernandoRevilla
- Feb 28th 2011, 05:51 AMAckbeet
Yeah, that. Right.