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Math Help - Help on solving differential equation

  1. #1
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    Help on solving differential equation

    The problem says, "Solve the differential equation. Assume a, b, and k are nonzero constants."

    dP
    dt = P - a



    Here is how I tried to solve the problem:


    dP
    dt = P - a

    multiply both sides by dt:

    dp = P - a dt

    divide both sides by P:

    1/P dP = -a dt

    take integral of both sides:

    (integral sign) 1/P dP = (integral sign) -a dt

    ln|P| = -at + C

    exponentiate both sides to get rid of natural log:

    e^(ln|P|) = e^(-at) * e^(C)

    P = Ce^(-at) <----This is my answer, where C is just a constant.

    However, my book says that the answer is P = a + Ae^(t). Please let me know what I did wrong. Thank you


    Last edited by NeedsHelpPlease; August 9th 2012 at 01:00 PM.
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  2. #2
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    Re: Help on solving differential equation

    Never mind. I think I figured out what I did wrong. I wasn't supposed to dived by P. I needed to divide by P-a and do a u-substitution
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