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Math Help - what is this?

  1. #1
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    what is this?

    What type of DE is this:

    xy'=y(1-ln\frac{x}{y})

    Should I solve it by substitution or any other way?
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  2. #2
    Junior Member
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    i think you should try dividing by x and then y=zx
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  3. #3
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    I have tried many methods but don't know what to do with 'ln' to separate y and x
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  4. #4
    Super Member Deadstar's Avatar
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    Quote Originally Posted by hekt View Post
    I have tried many methods but don't know what to do with 'ln' to separate y and x
    \ln \left (\frac{x}{y} \right) = \ln(x) - \ln(y)
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  5. #5
    MHF Contributor chisigma's Avatar
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    Thi type of DE was examined in the eighteen century by the Italian mathematician Gabriele Manfredi and is commonly know as 'homogeneous differrential equation'. Is is written as...

    y^{'} = f (x,y) = f(1,\frac{y}{x}) (1)

    ... and with the substitution \frac{y}{x} = t and some steps it assumes the form...

    \frac{dt}{f(1,t)-t} = \frac{dx}{x} (2)

    ... so that the variables are separated...

    Kind regards

    \chi \sigma
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