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Math Help - differential equation problem

  1. #1
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    Exclamation differential equation problem

    I'm not quite sure how to solve this problem. I tried one step but don't know what to do next. It seems weird.

    dw/dt=-lambdaW(t) with W(0)=Winitial

    All I did was separate:

    dw/-lambdaW(t)=dt but don't now what to do from here because I don't know what W(t) is.

    Can anyone help? I will deeply appreciate it! thank you!
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by swimmergirl View Post
    I'm not quite sure how to solve this problem. I tried one step but don't know what to do next. It seems weird.

    dw/dt=-lambdaW(t) with W(0)=Winitial

    All I did was separate:

    dw/-lambdaW(t)=dt but don't now what to do from here because I don't know what W(t) is.

    Can anyone help? I will deeply appreciate it! thank you!
    Do you mean:

    \frac{dw}{dt}=-\lambda w ?

    CB
    Last edited by CaptainBlack; February 20th 2009 at 02:02 AM.
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  3. #3
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    the problem in the book says what i originally wrote but i guess it makes sense to write it just as W instead of W(t)
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by swimmergirl View Post
    the problem in the book says what i originally wrote but i guess it makes sense to write it just as W instead of W(t)
    Then the solution is:

    \int \frac{1}{w} \ dw=- \lambda \int \ dt

    with the initial condition determining the constant of integrations.

    CB
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