Solving Sys of Difeq: Matrix, Eigen Values, Det, Calculus, Algebra

[marmot]

Homework Statement

http://img412.imageshack.us/img412/6463/difeq.jpg

Homework Equations

Matrix maniupation, egein values, determinant, etc

The Attempt at a Solution

Well, at first I tried the formulaic way, i.e. finding the eigenvalue through the determinant, but it gave me zero and worse when plugged in it gives zero for x1 and x2.

It seems it is too simple to use matrixes here so Instead I just tried it the old fashioned way - i.e. solving for the system through calculus and algebra.

So

x1'=-20x1
x2'=-10x1

So I solved for x1 because it seemed pretty straightforward and it was, I got:

x1=8exp(-20t)

which is correct

So now I try plugging it in x2' and integrating dx2/dt and I get

x2-8=2exp(-20t)/5-2/5

which should give

x2=2exp(-20t)/5-2/5+8

However this is wrong. can someone help me with this?

 

[Pengwuino]

When you plugged in x1, you forgot to multiply by -10 and your integration came out incorrectly.

Also, an eigenvalue of 0 is perfectly acceptable. It's simply a constant solution.