1. The problem statement, all variables and given/known data du/dt=(d^2 u)/dx^2+1 u(x,0)=f(x) du/dx (0,t)=1 du/dx (L,t)=B du/dt=0 Determine an equilibrium temperature distribution. For what value of B is there a solution? 2. Relevant equations Not really sure what to put here. 3. The attempt at a solution I started by trying to separate variables, with u(x,t)=phi(x)*g(t), and got to g'(t)/g(t)=phi''(x)/phi(x)+1/(phi(x)g(t))=0. So g(t) is constant based on the above, but then I get a little lost while trying to solve for phi. I tried letting g(t)=lamda (abbreviated lm from now on), and got phi''(t)+1/lm=0, which yields a quadratic solution of [(-lm*x^2)/2+x/lm+C/lm] after using the condition du/dx (0,t)=1. Then, since this is phi(x), u(x,t)= -lm^2*x^2/2+ x + lm*C. Using the other condition du/dx (L,t)=B, and assuming some quick mental algebra was correct, B=-lm^2*L+1. First off, is all of the above a correct approach as far as you can tell? And secondly, do I need to find u(x,t) or a specific value of lm?