Use the Laplace transform to solve the given initial-value problem. y' + 3y = et, y(0) = 2 y(t) = [13e -37 + ebt] X Need Help? Read It Master It [-/1 Points] DETAILS ZILLDIFFEQ9 7.2.040. Use the Laplace transform to solve the given initial-value problem. y" - 3y' = 8e2t - 2e-t, y(0) = 1, y'(0) = -1 y(t) = Need Help? Read It Watch It16. [0/1 Points] DETAILS PREVIOUS ANSWERS ZILLDIFFEQ9 7.2.043. Use the Laplace transform to solve the given initial-value problem. 2y" + 3y" - 3y' - 2y = e-, y(0) = 0, y'(0) = 0, y"(0) = 1 3 130COs (3t) - ~ sin ( 3t) + 16 -2t 13 y(t) = + 13 t 39 20 60 X Need Help? Read It 17. [0/1 Points] DETAILS PREVIOUS ANSWERS ZILLDIFFEQ9 7.2.044. Use the Laplace transform to solve the given initial-value problem. y"" + 2y" - y' - 2y = sin(3t), y(0) = 0, y'(0) = 0, y"(0) = 1 3 13 y(t) = 130COS ( 3t) - 6 sin (3t) + 16 -2t -t + 13 39 e 20 60 X Need Help? Read ItThe inverse forms of the results in Problem 49 in Exercises 7.1 are s - a = eat cos bt (s - a ) 2+ 62 and b eat sin bt. ( s - a ) 2 + 2 s Use the Laplace transform and these inverses to solve the given initial-value problem. y' ty = e-4 cos 3t, y(0) = 0 y(t) = "le * -e-#(cos 3t + sin 3t) ] X