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help with differential euqation

Posted on 2014-04-24
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I reading the solution of a dif eq
Y'' -m^2 *n^2 * y =

Y = c1e1 ^ ( -mny) + c2e2 ^ ( + mny )
how did he get this result ?

and X'' + n^2X
then X = c3 sin nx + c4 cosnx
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Question by:c_hockland
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by:d-glitch
ID: 40022534
Could you post a scan or photo of the actual equations?

I still might not be able to help, but the text form of complex math is an additional and unpleasant hurdle.
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BigRat earned 500 total points
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Taking the second equation first, y'' + n²y = 0, and substitute y = A*exp(bt) you get :-

      A*b*b*exp(bt) + n²*A*exp(bt) = 0

and this can only be so if b²=-n² and this only if b = i*n where i is the square root of -1.
(Because e to the power of anyting is NEVER zero, and A=0 is a tribial solution)

And n can be positive of negative, since it square is aloways positive, so the exponentials are exp(int) and exp(-int), and it you remember your trig, this is sin(nt) and cos(nt) and hence the result.

So back into the first equation where n² is m²*n² and presto the result.
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