I am trying to find the steady state temp for the following Partial Diff. Eqn:
Ut = (alpha)^2 * Uxx - (beta)U
BCs: U(0,t) = 1 and U(1,t) = 1.
I know how to approach the problem, but I am getting stuck on the Integrating U. Here is what I have:
1.) SETUP OF PROBLEM
steady-state => Ut = 0, so
(alpha)^2 * Uxx - (beta)U = 0
(alpha)^2 * Uxx = (beta)U
Integral((alpha)^2 * Uxx)dx = Integral ((beta)U)dx
((alpha)^2 * Ux = (beta) * How do I do [Integral(U) dx] ????
This is where I get stuck, so if you could please show me how to Integrate(U) dx or what I need to do to fix this? Thanks for any and all help.