Hi, it is easy solving these PDEs with the idealized homogeneous BCs they throw out in class, but I am having some difficulty solving the transient problem posed in the images below. I have tried working through it, but I don't have confidence in the result. I overlook the solution when the eigenvalues are 0 because that results in the derivative boundary conditions having to equal each other at all times, which is not true for the problem at hand. I also took the cosh and sinh route when the the eigenvalues are negative, but that was giving me similar C1 and C2 formulations as when the eigenvalues are positive. May I please get some direction as to where I'm going wrong? Does the end result make sense? I don't mind not solving for eigenvalues now as the intention is to have a symbolic representation. Thank you very much.