# Homogenous diff. equation and exponential matrix

1. Sep 25, 2008

### Mathman23

1. The problem statement, all variables and given/known data

Howdy,

Given a matrix $$\left[\begin{array}{ccc}x_{11} & x_{12}\\x_{21} & x_{12}\end{array}\right]$$

Which has the exponential matrix $$e^{t\cdot a}$$

When given the eqn $$x'= Ax + b$$ where $$b = \left[\begin{array}{c}b_1 \\ b_2\end{array}\right]$$

I know that had it only been x' = Ax, then solution would be $$x = e^{ta} \cdot C$$ where C is a constant.

Could someone here please be so kind to assist me in which secret formula do I use to expres the solution of the system x' = Ax+b??

Cheers
Fred

2. Sep 25, 2008