# Laplace transforms

1. May 10, 2010

### squenshl

I'm deriving the heat equation using Laplace transforms.
I'm up to u(bar) = Aesqrt(s)x + Be-sqrt(s)x.
My boundary conditions are lim(x tends to 0) = 0 & this makes A = 0, so u(bar) = Be-sqrt(s)x
My other BC is ux(0,t) = -Q
My question is how do I get B using this BC?
I tried using the def of Laplace transforms and get -dQ(bar)/dx

Last edited: May 10, 2010
2. May 10, 2010

### squenshl

I got B = Q/sqrt(s) and this implies that U(bar) = Qe-sqrt(s)x/sqrt(s), I hope thats right