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Math Help - Differential equation problem

  1. #1
    Member
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    Dec 2007
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    Differential equation problem

    I need to find the equation of the curve that satisfies the differential equation dy/dx = y / x(x-1) and passes through the point (1,2)

    To start i worked out that

    1/y dy/dx = 1 / x(x-1)

    i tried to integrate and got

    lny = ln x(x-1) but i am not sure if that is right or what else to do


    thanks
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  2. #2
    MHF Contributor
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    France
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    Hi

    Your integration on x side is not correct

    \int \frac{1}{x(x-1)}dx = \int \left(\frac{1}{x-1} - \frac{1}{x}\right)dx = \ln \frac{|x-1|}{|x|}
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  3. #3
    Member
    Joined
    Jan 2009
    Posts
    105
    Quote Originally Posted by gracey View Post
    I need to find the equation of the curve that satisfies the differential equation dy/dx = y / x(x-1) and passes through the point (1,2)

    To start i worked out that

    1/y dy/dx = 1 / x(x-1)

    i tried to integrate and got

    lny = ln x(x-1) but i am not sure if that is right or what else to do


    thanks
    Did you differentiate \ln x(x - 1) as a check? Do you get back \frac{1}{x(x - 1)} ? (If you answer yes to this question then you need to seriously review differentiation).

    The right hand side must be integrated using a partial fraction decomposition: \frac{1}{x (x - 1)} = \frac{1}{x - 1} - \frac{1}{x}.
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