Please need an answer asap

Find the Laplace transform of t2 sin(5t). L{ta sin(5t)} = Find the Laplace transform of test sin(2t). Lite3t sin(2t) } Use the Laplace transform to solve the following initial value problem: x' = 5x + 2y, y = -3x + et I(0) = 0, y(0) =0 Let X(s) = [{x(t) }, and Y(s) = [ty(t)}. Find the expressions you obtain by taking the Laplace transform of both differential equations and solving for Y(s) and X(s): X(s) = Y(s) = Find the partial fraction decomposition of X(s) and Y(s) and their inverse Laplace transforms to find the solution of the system of DEs: I(t) = y(t) =). onsider the initial value problem y' + 49y = cos(7t), y(0) = 7, /(0) = 2. a. Take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation. Denote the Laplace transform of y(t) by Y(s). Do not move any terms from one side of the equation to the other (until you get to part (b) below) =0help (formulas) b. Solve your equation for Y(s). Y(s) = [ty(t)) = c. Take the inverse Laplace transform of both sides of the previous equation to solve for y(t). y(t) =