The discussion revolves around proving the relationship between the Laplace transform of a function scaled by a constant factor and the Laplace transform of the original function. Specifically, the original poster seeks to demonstrate that L{f(t/b)} = bF(bs) for b ≠ 0, focusing on the transformation of the variable within the integral.
Participants are actively engaging with the problem, exploring substitution techniques and the implications of changing variables in the context of the Laplace transform. Guidance has been provided regarding the necessary adjustments to the exponential term and the differential, indicating a productive direction in the discussion.
There is an emphasis on ensuring that the transformations adhere to the rules of calculus, particularly concerning the handling of differentials during substitution. The original poster has not yet provided a complete solution, and the discussion remains focused on the steps involved in the proof.
magnifik said:do i also have to plug in (t/b) into e-st so that it becomes e-s(t/b) ?
magnifik said:so..
u = t/b
t = bu
e^(-st)
e^(-sbu)