Homogeneous ODE system, how to solve using WOLFRAM

1. Dec 8, 2012

kougou

Hi.

If I have a homogeneous ODE with constant coefficient system in the form of 2x2 matrix:

X'=A X, A is a 2x2 matrix.

How do I solve this using wolfram or matlab?

2. Dec 8, 2012

Dustinsfl

What is the system explicitly?

3. Dec 8, 2012

kougou

Say

X'= [2, 4] X.
[1, 1]

A with with 2,4 in the top rows, and 1,1 in the bottom rows.

How do I use wolfram or matlab to solve this system?

4. Dec 8, 2012

Dustinsfl

We can re-write the system as
\begin{alignat*}{5}
x' & = & 2x+4y & = & 0\\
y' & = & x + y & = & 0
\end{alignat*}

DSolve[{x'[t]==2x[t]+4y[t],y'[t]==x[t]+y[t], Initial Conditions here},{x[t],y[t]},t]

5. Dec 8, 2012

Ray Vickson

I do not have access to Matlab, so I don't know the answer to the following: does Matlab have a exp(A) function for a matrix A? If so, we have X(t) = X(0) exp(A*t).