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Math Help - separable equations

  1. #1
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    separable equations

    Given the problem du/dt = e^(6u+2t)

    i cant seem to separate the two variables

    i tried using the natural logarithm of both sides but only got

    ln(du)=(6u+2t)*ln(dt)
    Last edited by washerman; October 2nd 2010 at 09:22 PM.
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  2. #2
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    Use the index law a^{m + n} = a^m a^n to simplify the exponential.
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  3. #3
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    edit:
    using the index law i was able to get it down to

    \dfrac{e^-^6^u}{-6} = \dfrac{e^2^t}{2} + C

    i was given the initial conditions of u(0) = 12

    and got  C = \dfrac{-e^-^7^2}{6}-\dfrac{1}{2}

    after putting it back in the equation and putting it in terms of u

    i got to the end and got  u = \dfrac{ln((-3e^2^t)+(e^-^7^2)-3)}{-6}

    but seems to be the wrong answer still.
    Last edited by washerman; October 2nd 2010 at 10:18 PM.
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  4. #4
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    You've lost a sign. That final "-3" in the numerator should be positive. I would recommend making the entire fraction negative rather than having the negative sign in the denominator although that is, of course, the same result.
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  5. #5
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    o sweet, finally got it right. Thank you!
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