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Thread: general solution of differential equation

  1. #1
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    general solution of differential equation

    $\displaystyle \frac{dy}{dx} = x(1-x) $

    $\displaystyle dy = x(1-x) dx $

    $\displaystyle dy = x-x^{2} dx $

    $\displaystyle \int dy = \int x-x^{2} dx $

    is this so far correct? cuse my book gives me a solution like this $\displaystyle \int \frac{1}{x(1-x)} = \int dy $

    And i have no idea how they got this?
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  2. #2
    MHF Contributor

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    Re: general solution of differential equation

    what you have written is correct. But are you sure you have copied the problem correctly? If the problem were
    $\displaystyle \frac{dy}{dx}= y- y^2$ then you would have $\displaystyle \int\frac{dy}{y- y^2}= \int dx$.
    Thanks from Tweety
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