1. The problem statement, all variables and given/known data The function u(x,t) satisfies the equation (1) = for 0 < x < pi, t > 0 and the boundary conditions (2) (0,t) = (pi, t) = 0 Show that (1) and (2) satisfy the superposition principle. 2. The attempt at a solution I let w(x,t) = au(x,t) + bv(x,t) for two constants a and b. = + = + = , where c is a constant Have I now showed that w(x,t) satisfies (1)? is not equal to unless c is 1...
You have not shown that w(x,t) satisfies (1). May I ask what " is not equal to unless c is 1..." have to do with the superposition principle? The part that is going about it correctly is when you do the following: " + = + ". But you need to prove that to be true, you can't just write it down... By the way, are you studying waves at the moment, because part 1 is part of the definition of a wave... -blazed