Let the ordinary differential equation
y'' + 6y' + 9y = 3e-3t
for unknown function y = y(t).
i) Using direct method (not Laplace transform) determine general solution to the problem.
ii) Use Laplace transform to solve corresponding initial value problem
y'' + 6y' + 9y = 3e-3t ; y(0) = -1; y'(0) = 1 .