1. The problem statement, all variables and given/known data Hi all. I am given the following differential equation: X'' - k*X=0. I am told that k = -m^2, so the general solution is given by: X = a*cos(m*x)+b*sin(m*x), where a and b are constants. I am also given boundary conditions: 1) X(-Pi) = X(Pi) 2) X'(-Pi) = X'(Pi). To satisfy #1, m must be an integer. But in my book the author states that in order to satisfy #1 and #2, m must be a positive integer. But I don't understand why m must be positive, because cosine is even.