1. Integrate (by calculus): u''(x) = -4u(x), 0 < x < pi 2. The attempt at a solution I'm not really sure where to start on this one is my problem. I can see that it won't be a e^2x problem because of the negative, which leads me to believe that it will deal with the positive/negative relationship involved when you differentiate cos. The answer is u(x) = c1sin(2x) + c2cos(2x) which makes sense since u'(x) = 2cos(2x) - 2sin(2x) and u''(x) = -4sin(2x) - 4cos(2x) = -4(sin(2x) + cos(2x)) = -4u(x) But, how do I go about showing my work? How am I supposed to know it's c1sin(2x) + c2cos(2x) in the first place?