1. The problem statement, all variables and given/known data Find U(x,t) dU/dt = d2U/dx2 + sin x Boundary Conditions: dU/dx (0,t) = 0 and U(1,t) = 0 Initial Condition: U(x,0) = cos 7*π*x 2. The attempt at a solution I start off with: d2(Un)/dx2 = λnUn (as an initial value problem) [d(Un)/dx](0) = 0; [d(Un)/dx](1) = 0 My teacher told me to use the orthogonality later on, but at this point I'm stuck. Can anyone enlighten me? Thanks!