Question: dsolve vs. Eigenvalue/Eigenvector

I am trying to solve a nonhomogenous linear system. I am first trying to first solve the corresponding homogeneous case. I have Maple12, so I first entered the 5x5 matrix and said Eigenvalues(A) and Eigenvectors(A). This yielded two complex and three real eigenvalues. However, when I typed the system of equations and used dsolve of the system, it gave me all real eigenvalues. I have tripled checked my inputs and they match... why the discrepancy? When I tried odetest it did not yield zeros, but I can't see where the problem lies.

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