Hi all. Lets solve the following ODE by using Laplace transforms [tex] y'' - y' = \exp(-x), [/tex] where y depends on x. Laplace-transforming we obtain (where Y denotes the Laplace-transformed of y) [tex] s^2Y(s)-sy(0)-y'(0) - sY(0) - y(0) = \ldots [/tex] My question is, why we are allowed to do this? Because when I Laplace transform y'', then we get some expression dependent on the variable s, but when we Laplace transform y', then we get an expression dependent on some other variable t, and likewise for the RHS. Who says that s=t? And then there's also the variable from transforming the RHS.