Math Help - Eigenvalues and Eigenvactors

1. Eigenvalues and Eigenvactors

Here is the question http://i1225.photobucket.com/albums/..._19/Eigen2.jpg

The second term should be De^( - √(5)t), I made a mistake when writing out the question.
I worked the answer out to be 3.09

Could someone verify that, I just want to be sure I have a good grasp on these type of questions.

thank you

2. Not quite. I do NOT get "3.09" but something similar. Show your work and perhaps we can point out an error.