I've done this question but I'm unsure if I used the boundary conditions right. The question is:
Find u(x,t) given u_xx=0 0<x<1, t>0 with boundary conditions u(0,t) = sin(t), u(1,t) = 0.5 t>0
To solve this question I found u = cx + f(t) where f(t) is any differentiable equation of t by integrating twice. I then used the boundary conditions to find c in terms of t. Is this correct?