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Homework Help: DE with substitution

  1. Oct 30, 2009 #1
    1. The problem statement, all variables and given/known data

    y' = cos(x-y)

    2. Relevant equations

    3. The attempt at a solution

    Using x-y=t and solving the integrals, I get that the general solution is:
    -cot(0.5(x-y)) = x + c which is correct, but there's another solution which is x-y=2πk, but I don't understand why.
    In the integral I get that it is undefined for 1-cost=0.
    Meaning it is undefined for cost = 1, or cos(x-y) = 1.
    Plugging it in the original problem to see if it satisfied it gives me y' = 1. How can I know if this is true for all y (I guess it is)...
    I didn't exactly understand what do I need to do here.
  2. jcsd
  3. Oct 30, 2009 #2
    if you want to check that y'=1 you best start with the definition of y...which is just x-2πk...
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