After having solved the one-dimensional heat equation, we will briefly summarize some solutions to similar problems, which, as we will see, we can apply fairly often. In the following we assume the function sought to be f (x). We will also discuss the various cases of boundary conditions that may apply.
For all values of λ the general solution for this problem is
irrespective of the boundary conditions. See section 8.2.3 for details on this.