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Seperable Differential Equations, Multiplicative Constant Confusion! Help Clarify!

  1. Dec 21, 2011 #1
    I curiously never had a problem solving Seperable Equations in the Seperable Equations chapter of the Boyce/Diprima book. I am the kind of person who likes to do things the long way, and encountered a problem solving for an Integrating Factor(Linear ODE, NOT EXACT) the long proofy way. I tend not to use the (e^(INT)p(x)dx) formula. Formulas are too easy to forget.

    In solving for the integrating factor, I came upon an easy seperable equation of course! I split this one up a little differently than usually, still correctly I think? I came up with an answer that differs from the formula approach.

    Is the 1/3 absorbed by the constant or something?
    PDF ATTACHED

    Thanks,

    Dane
     

    Attached Files:

  2. jcsd
  3. Dec 21, 2011 #2

    epenguin

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    Re: Seperable Differential Equations, Multiplicative Constant Confusion! Help Clarify

    Yes you could say they are equal. I prefer to say they are the same thing - and if you wrote 15K3 instead of K1 it would the same thing. At this stage they are both arbitrary, in a sense they are not anything. When you make conform to an initial condition you will get the same result from either of them.
     
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