So on this practice exam paper problem #5 (page 7) http://www.math.lsa.umich.edu/course...inalW10sol.pdf
I am told to find the Laplace Transform of:
tx''-3x'+x=0 where x(0)=0
Now I've always transformed tx'' in the following way:
Transform of tx'' -> -[(s^2)*X(s)-x'(0)]'
So I would get -[(2*s*X(s))+((s^2)*X'(s)))]
But the solution gives tx'' -> -(s*X(s)-x(0))'
Which gives -[(s*X'(s))+x(s)]
Even on my textbook: Differential Equations: Computing and Modelling by Edwards & Penney they are using the method that I have always used.