Question

Laplace: L{t*cos(2t)}. I know that L{t*f(t)}=-d/ds F(s) where F(s) is the Laplace transform of f(t). So then L{t*f(t)}=-d/ds * s/(s^2+4) and if I use the quotient rule I get the result [-(s^2+4)-2s^2]/2s. However, the answer is supposed to be (s^2-4)/(s^2+4)^2. How did they come up with that answer? Part of the instructions before this set of problems says that "A preliminary integration by parts may be necessary." Might that apply to my problem? I'm not sure how I would implement integration by parts in a Laplace...

Answer 1

Anyone?

Answer 2

You have the rule related to Laplace transforms correct. But what you haven't done is differentiate s/(s^2 + 4) correctly.