Consider the system of differential equations r' = 4x - 2y y' = 5x - 2y. Show that it has eigenvalues A = 1 + i and associated eigenvectors v = 5 Write down the general real solution of this system. Find the specific solution if r(0) = 1 and y (0) = 1. Consider the system of differential equations x =-cty y' = -6x + 4y. Determine all eigenvalues associated with the system. Determine the eigenvectors associated with each eigenvalue. Write down the general solution to the system. Find the particular solution satisfying x(0) = 2 and y(0) = 3