1. The problem statement, all variables and given/known data Find the steady state (equilibrium) solution for the following boundary value problem: ∂u/∂t = (1/2)∂2u/∂x2 Boundary condition: u(0,t) = 0 and u(1,t) = -1 Initial condition: u(x,0) = 0 2. Relevant equations u(x,t) = Φ(x)G(t) 3. The attempt at a solution I have found the solution for Φ(x) and G(t) but when implementing the boundary condition u(1,t) = -1 I have that u(1,t) = Φ(1)G(t)=-1. My question is whether or not I should assume that G(t) = -1 and not Φ(1). The reason I ask is because the steady state solution should not depend on time, therefore G(t) needs to be a constant. However I don't trust this assumption and that leads me to a more general question which is: How am I supposed to know which function to make equal to the right hand side of the equation? I mean in any case where you can split a function (for example) u(x,t) = Φ(x)G(t) and have a boundary condition. In other words, if this problem didn't specify that the solution should be a steady state solution then what would you do when trying to figure out which function is equal to the right hand side?