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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 apositiveinteger. But I don't understand why m must be positive, because cosine is even.

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# Homework Help: Diff. eq. and boundary conditions

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