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

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**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....