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?
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!
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 =
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...