We have a question:

Question

X'={{1,0,0} {-4,1,0} {3,6,2}}X; X(0)={-1,2,-30}

I have worked out to the general solution but I don't think it's right. I have:
X=C1 {0,0,1}e^2t + C2 {0,-1,6} e^t + C3 [{0,-2,6} + {0,-1,6}t] e^t

this gives me x(t)=0....

Answer 1

hmmm. There do seem to be too many zeros to make things work out right.

Answer 2

However, at

http://www.wolframalpha.com/widgets/gallery/view.jsp?id=ef7f9b7e172cd67fb8f192f29fc1e483

it gets a solution apparently involving eigenvalues -1 and 3