HW08: Problem 11 (1 point) In this exercise we will use the Laplace transform to solve the following initial value problem: _ 9, 0t2 __ __ may{0, 2g , yror walr 9 (1) First, using Y fortne Laplace transform of Mt}, i_e_, Y = [y[t)), nd the equation obtained by taking the Laplace transform of the initial value problem snrzi'r + 2s +91\" +9 = as Se\"(2s}!s (2) Next solve for Y = us -33rrsnr2)+9) -9f(s\"{2)+9) - e\"(-2s)ts + se"(-2s)r'(s*{2)+9 (3) Finally apply the inverse Laplace transform to nd y) y(t) = 13cos(3t}3sin(3t}+u(t2) +u[t2)cos(3t6)