# Math Help - boundary value problem PDE

1. ## 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.

2. 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.
If you let $u(x,t) = e^{-2t} v(x,t)$ then the PDE becomes
$v_t = v_{xx}$