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Math Help - Differentiable Eq. finding function f

  1. #1
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    Differentiable Eq. finding function f

    Find the function f such that f'(x) = f(x)(1 - f(x)) and f(0) = \frac{1}{2}.

    We are currently covering separable differentiable eq. and this problem is throwing me for a loop.

    Any hints for a starting point?

    I know
    f(x) = \int(f(x)(1 - f(x))) thus \frac{1}{2} = \int(f(0)(1 - f(0))). Then I am lost. How can you find f if you can't separate the x's and y's?
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  2. #2
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    Quote Originally Posted by diablo2121 View Post
    Find the function f such that f'(x) = f(x)(1 - f(x)) and f(0) = \frac{1}{2}.

    We are currently covering separable differentiable eq. and this problem is throwing me for a loop.

    Any hints for a starting point?

    I know
    f(x) = \int(f(x)(1 - f(x))) thus \frac{1}{2} = \int(f(0)(1 - f(0))). Then I am lost. How can you find f if you can't separate the x's and y's?
    You might find the problem easier by using the following notation:


    Solve \frac{dy}{dx} = y(1 - y) where y = \frac{1}{2} when x = 0.
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