I am having a lot of problems with these sorts of questions..help please!
u_t = alpha^2*u_xx + sin(2x)
u(−pi, t) = u(pi, t), u_x(−pi, t) = u_x(pi, t)
u(x, 0) = cos(x)
Solve the problem by eigenfunction expansion
I don't know how to deal with the boundary conditions. I am used to seeing the BC being u(x,t)=0, u(L,t)=4 or similar but never having the BC equal to each other.
I don't know how to deal with the r. Do i treat both the r and k as constants?
Help is greatly appreciated. Please be as detailed as possible, I am not very comfortable with these types of problems.