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Question concerning constants of integration

  1. Feb 7, 2013 #1
    1. The problem statement, all variables and given/known data

    How can one simply let C=lnk? Thus changing

    y=[itex]\pm[/itex][itex]\sqrt{ln(t^{2}+1)+C}[/itex]

    to

    y=[itex]\pm[/itex][itex]\sqrt{ln[k(t^{2}+1)]}[/itex]

    2. Relevant equations

    None

    3. The attempt at a solution

    I know they are both arbitrary constants, are there restrictions on the allowed values of the constants? Actually I checked the answer in the book and it said k is allowed to be any positive real number. I understand because it is under the radical. Insight into this would be helpful.
     
  2. jcsd
  3. Feb 7, 2013 #2

    pasmith

    User Avatar
    Homework Helper

    For every real [itex]C[/itex], there exists a unique [itex]k > 0[/itex] such that [itex]C = \ln k[/itex]. Thus one can always replace an arbitrary constant [itex]C[/itex] with [itex]\ln k[/itex] where [itex]k > 0[/itex] is arbitrary.
     
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