Thread: Laplace transforms View Single Post
 Math Emeritus Sci Advisor Thanks PF Gold P: 39,345 The point is that all three methods: a)$$\displaystyle \mathcal{L}[e^{at}f(t)] = F(s-a),$$ where F(s) is the Laplace transform of t. b)$$\displaystyle \mathcal{L}[tf(t)]= -F'(s)$$ where F(s) is the Laplace transform of $e^{3t}$. c)$$\displaystyle \mathcal{L}[te^{at}]= \int_0^\infty te^{(-s+3)t}dt$$ will give the same result. It would be a good exercise to try each method and see.