Please help! I need to find the solution to the system x' = 6y, y' = -5x, with the initial conditions being x(0) = 1, y(0)= 5. I believe I have to do eigenvalues, but my eqns aren't coming out right.

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What eigenvalues have you found?

I think I have found lambda equals +/- sqrt(30), based on my matrix: [0- lambda, 6; -5, 0-lambda]

+- sqrt(30) i
They are imaginary.

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