Can you please provide solutions for questions 6 & 7?

Find the Laplace transform of the following functions. (a) f(t) = sin(2t) cos(2t) (h) f(t) : 66'\" sin(3t) (C) f(t) = 6te'2t sin(3t) (d) t) I tzeg't Find the inverse Laplace transform: a (a) Frs) 1-5-6 _ 4 (1)) F05) _ (s+2)(52+9) _ 5+4- (0) PIS) _ 52+4s+29 The transform of the solution to a certain differential equation is given by Y(s) : 3:; Determine the solution y(t) of the differential equation. Suppose that the function y(t) satises the DE y\" 7 2y' 7 y = 35in(4t), with initial values y(0) = *1, y'(0) = 1. Find the Laplace transform of y(t). Consider the following IVP: y\" + 631' + 13y = 0, y(0) = 2, y'(0) = 1. (:1) Find the Laplace transform of the solution y(t). (13) Find the solution y(t) by inverting the transform. Consider the following NP: y" 3y' 10y = 5, y(0) = 2, y'(0) = 4. (:1) Find the Laplace transform of the solution y(t). (in) Find the solution y(t) by inverting the transform