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Math Help - Simple but conceptual question

  1. #1
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    Simple but conceptual question

    So I may just be rusty on my algebra, but I'm covering differential equations at a basic level right now and I've seen this pop up a few times and I'd love to know the proof behind why.

    I'll see either 10-x=e^{-kt-c1} become x=10-Ce^{-kt} or say y+4=e^{\frac{-x^2}{2}+C1} become y+4=Ce^{\frac{-x^2}{2}}

    I just don't quite see how they're pulling that C down and in front of the exponential function...can anyone offer a proof or other explanation as to why? Thanks!
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  2. #2
    Super Member Aryth's Avatar
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    In the equations you're giving, they are using little c's... The big C stands for:

     C = \pm e^{c_1}

    Or e to the power of some constant... Since that does not change it's constancy, it's valid.

    In most basic differential equations, the C becomes the initial value anyway.

    For example:

    10 - x = e^{-kt - c_1}

    10 - x = e^{-kt}e^{-c_1}

    C = e^{-c_1}

    10 - x = Ce^{-kt}

    10 - Ce^{-kt} = x
    Last edited by Aryth; April 18th 2008 at 11:17 PM.
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