Differential Equation eigenvalue!!

Hi, I am having trouble with the following problem. I dont know where I am doing it wrong... please help me out...

**Problem:**

Apply the eigenvalue method to find the particular solution to the system of differential equations

which satifies the initial conditions

https://instruct.math.lsa.umich.edu/...f2f7c67ce1.png

**Attempt:**

So I found the eigenvalues and solved for eigenvector.

So for lambda = 13 eigenvector

for lambda = 1 eigenvector

Now for the given initial conditions I finally got:

x1 = -16/3*e^(13t) - 7/3*e^(t)

x2 = -16/3*e^(13t) + 5/3*e^(t)

But its wrong...

Please help...

Many Thanks....