f3. (i) The book discusses the convolution of functions and

how the LaPlace transform interacts with the convolution. In

each of these two cases compute the convolution of f and g, the

LaPlace transforms of f and g, and verify the product formula for

the LaPlace transform of a convolution is correct.

(ii) Suppose we wish to solve the differential equation y"

+3y"-4 y'=ex. Explain why we can't use the LaPlace transform to solve this problem. How would you solve it? (You don't

have to work out the solutions, just describe a method that

should be useful.)