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Math Help - seperation of variables

  1. #1
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    seperation of variables

    Help! I can't figure out this problem:

    Find f(x), when cos^2(x)f'(x) = e^-f(x), and f(0) = 0.5

    I have several other questions which I am lost on so I will be posting several! Thanks!
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  2. #2
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    Quote Originally Posted by geode View Post
    Help! I can't figure out this problem:

    Find f(x), when cos^2(x)f'(x) = e^-f(x), and f(0) = 0.5

    I have several other questions which I am lost on so I will be posting several! Thanks!
    Let say we want to solve,
    \cos^2 x f'(x) = e^{-f(x)} \mbox{ on }(0,\pi/2)
    Then,
    \frac{f'(x)}{e^{-f(x)}} = \sec^2 x

    This is a seperable differencial equation.
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