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Thread: Integration / Splitting the variables

  1. #1
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    [SOLVED] Integration / Splitting the variables

    Hey, I've gotta brush up on my integration / differentiation before the september term and have come across a question that's giving me trouble (well.. a few tbh but I might go back to them later..)

    $\displaystyle
    \frac{\delta x}{\delta t} = 3x
    $

    solve, given x=10, t=0
    Cut-down workings:

    rearrange and differentiate with respect to x
    $\displaystyle \int (\frac{1}{3} \frac{\delta x}{\delta t}) \delta x = \int (3x) \delta x$

    And this simplifies /rearranges to:
    $\displaystyle x = e^{3t+c}$

    Problem
    According to the textbook, the answer should be:
    $\displaystyle x = e^{3t+10}$


    The closest I've gotten so far is as follows:

    $\displaystyle \ln (x) = \ln e^{3t+c}$
    $\displaystyle \ln (x) = 3t+c$

    t is given in the question as 0, therefore:
    $\displaystyle c = \ln (x)$

    if $\displaystyle c = \ln (A)$, then
    $\displaystyle \ln (A) = \ln (x)$

    x is given as 10, therefore:

    $\displaystyle A = 10 $


    However, I'm probably going at it slightly wrong since I can't get A=10 to become c=10 ...


    Any help?

    Thanks,
    kwah
    Last edited by kwah; Sep 3rd 2008 at 06:46 AM.
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  2. #2
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    Quote Originally Posted by kwah View Post

    Problem
    According to the textbook, the answer should be:
    $\displaystyle x = e^{3t+10}$
    the text "solution" does not match up with the given initial condition ...
    x = 10 when t = 0

    I also get $\displaystyle x = 10e^{3t}$ ... maybe they meant to type $\displaystyle x = e^{3t + \ln{10}}$
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  3. #3
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    thanks... i think its just an error in the textbook =]
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