Thread: boundary value problem PDE

Can someone help me find X(x) and Y(y) for u = XY in this PDE:

ut = uxx - 2u
boundary conditions: u(0,t) = 0, u(3,t) = 0
initial condition: u(x,0) = 2sin(pi*x) - sin(4*pi*x)
I know how to do the separation of variables, but again I'm having trouble finding X and Y.
Thanks for your help.

Originally Posted by PvtBillPilgrim

Can someone help me find X(x) and Y(y) for u = XY in this PDE:

ut = uxx - 2u
boundary conditions: u(0,t) = 0, u(3,t) = 0
initial condition: u(x,0) = 2sin(pi*x) - sin(4*pi*x)
I know how to do the separation of variables, but again I'm having trouble finding X and Y.
Thanks for your help.

If you let then the PDE becomes



with the same IC's and BC's.