Sorry don't know how to use the partial symbol, bear with me
partial u wrt t=2*(2nd partial u wrt x)
partial u wrt x (0,t)=partial u wrt x (1,t)=0
I get an answer that is different than the solution manual, but I am convinced the solution manual is wrong, so I would just like it if anyone had the spare time to verify the solution for me. I do have a few minor questions though.
1. When solving for the eigenvalues, is n=0,1,2,3... or does n=1,2,3...? I ask this because I get 0 as an eigenvalue when doing the case for lambda=0, but technically this woulda already shown itself when I did the other case when I got the "real" eigenvalues because it was to solve sqrt(-lambda)=npi, so if n=0 that would have already been taken care of.
The Attempt at a Solution
I get F(x)=Cncosnpix and G(t)= e^(-2pi^2n^2t) When I solve the fourier series I used L=1 and got ao=-1/3 and an = (4(-1)^n) )/ (pi^2n^2)