(1 point) Transform the differential equation 5y" 5y' + 3y = = cosh(at) y(0) = -1 y' = 8 into an algebraic equation by taking the Laplace transform of each side. = Therefore Y = (1 point) Use the Laplace transform to solve the following initial value problem: = = = y" 6y' + 25y = 0 y(0) = 0, y'(0) = 4 First, using Y for the Laplace transform of y(t), i.e., Y = L{y(t)}, L find the equation you get by taking the Laplace transform of the differential equation = 0 Now solve for Y(s) = By completing the square in the denominator and inverting the transform, find g(t) = ) =