Solve the initial value problem below using the method of Laplace transforms. y" - 3y' - 18y = 0, y(0) = 1, y'(0) =51 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. What is the Laplace transform Y(s) of the solution y(t)? Y(S) =Solve the initial value problem below using the method of Laplace transforms. y" - 6y' + 34y = 116e , y(0) = 4, y'(0) =9 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. y(t) = (Type an exact answer in terms of e.)Solve the initial value problem below using the method of Laplace transforms. y"+ 8y' + 12y =90e", y(0) = - 7, y'(0) = 48 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. y(t) = (Type an exact answer in terms of e.)