Let a and c be nonzero real numbers and consider the differential equation ay" + y + cy=0 Color the point (a, c) in the ac-plane as follows: • Red if (*) with the given a and c values has a general solution of the form y = Aerit + Berat for real numbers r1 r2, A, and B. • Green if (*) with the given a and c values has a general solution of the form y = Aert + Btert for real numbers r, A, and B. Blue if (*) with the given a and c values has a general solution of the form y = Aeat cos(3t) + Beat sin(8t) for real numbers a, 3, A, and B. What does this coloring scheme produce in the ac-plane?

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