1. The problem statement, all variables and given/known data Currently working on a heat equation problem for an applied math class. I got a solution v(x,t) = Ʃn≥1(2/n∏)sin(n∏x)cos(n∏ct), x ε [0,1], t≥0, which seems wrong since, for any fixed x and t, v(x,t)=∞. 2. Relevant equations Governing equation is utt=c2uxx, where c is the speed of sound and u(x,t) is the longitudinal pressure distribution along a tube that is open at x=0 and has a rigid surface at x=1. The boundary condition at x=0 is u(0,t)=g(t)=cos(ωt) where ω is the frequency of the emitted sound. On the other hand, the rigid surface at x=1 implies a vanishing pressure at that point, and thus the boundary condition u(1,t)=0. Assume the initial conditions of utt=c2uxx are both zero. 3. The attempt at a solution I'm supposed to "Use the transformation u(x,t) = v(x,t) + ψ(x)g(t) to homogenize the boundary conditions by enforcing linearity on ψ." Then I'm supposed to "Solve for the homogeneous solution v1(x,t) of the transformed equation." I've checked over my work several times and I keep getting v1(x,t) = Ʃn≥1(2/n∏)sin(n∏x)cos(n∏ct), what has to be wrong. Thoughts? Concerns?