- #1
Scootertaj
- 97
- 0
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?
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?