Recent content by JoernE

Thanks MasterX! This should be \displaystyle X = A \cos(\sqrt{\lambda}x) + B \sin(\sqrt{\lambda}x) so \displaystyle X(\pi) = B \sin (\sqrt{\lambda} \pi) = 0 \displaystyle \ \sqrt{\lambda} \pi = \frac{n \pi }{2} \displaystyle \ \sqrt{\lambda} = \frac{n}{2} \displaystyle \...

Thanks. Are you referring to my first post here? Are you saying that what I wrote in the second post (under "I have a different method") is not correct?

I have a different method... Let u = w(x,t) + v(x) Then \frac{\partial u}{\partial t} = \frac{\partial w}{\partial t} and \frac{\partial^2 u}{\partial x^2} = \frac{\partial^2 w}{\partial x^2} + \frac{\partial^2 v}{\partial x^2} Sub these back into the PDE to obtain...

Consider the following non-homogenous heat equation on 0 \leq x \leq \pi u_t = k u_{xx} - 1 with u(x,0) = 0, u(0,t) = 0, u(\pi, t) = 0 Find a solution of the form \displaystyle \sum_1^{\infty} b_n(t) \phi_n (x) where \phi_n(x) are the eigenfunctions of an appropriate homogenous...