# Inhomogeniouse System

1. Aug 26, 2010

### AlinaR

Good afternoon!
I have a strange results solving this problem.

x'=[3,4;-1,-1]*x+[e^t;0], with init. cond. x(0)=[1;0].

x'=Ax+(e^(mu*t))*b thus mu=1, b=[1;0]

x(t)=(e^(mu*t))((mu*I-A)^-1)*b
x(t)=e^t*(([mu,0;0,mu]-[3,4;-1,-1])^-1)*b=e^t*([-2,-4;1,2]^-1)*[1;0]
But the problem is that [-2,-4;1,2]^-1 matrix is singular to working precision.

ans =

Inf Inf
Inf Inf

Is that some typo in the matrix or am I using the wrong way to solve this type of equations?

Thank you very much for any ideas!

Best regards,
Alina

2. Aug 26, 2010

### ross_tang

Hello. Please refer to my article in http://www.voofie.com/concept/Mathematics/" [Broken]:

http://www.voofie.com/content/18/solving-system-of-first-order-linear-differential-equations-with-matrix-exponential-method/" [Broken]

What you really need is matrix exponential, instead of matrix inverse. You can find example in another article:

http://www.voofie.com/content/19/a-worked-example-of-solving-system-of-first-order-linear-differential-equation/" [Broken]

Last edited by a moderator: May 4, 2017