Problem 11: Consider the following differential equation: y"-4y' + 4y = 2e2t - 12 cos(3t) - 5 sin(3t). a) What is the complementary solution? b) Suppose 91(t) = 2e2t. What should be your guess for Y₁(t) without actually solving for it? c) Now solve for Y₁(t). d) If g2(t) = -12 cos(3t) - 5 sin(3t), solve for Y2(t). e) Find the general solution of the differential equation. f) Find the particular solution given y(0) = -2 and y'(0) = 2.