Solve the heat equation with the boundary conditions and the following initial condition: .
Now, the question itself isn't a problem, its the actual derivation of the heat equation that is (its not asked in the question but we're told that in an exam it would be).
So I'm looking to derive this. where .
So i start by doing seperation of variables to get and .
Now at this point I think I should use eigenfunctions then superposition to solve it but i cant see where the or the come from?
Any help please?