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Math Help - Basic Diff EQ question: finding a function with given properties

  1. #1
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    Basic Diff EQ question: finding a function with given properties

    Find a function f(y) with the property that: for each solution y(x) of dy/dx = f(y), the limiting value lim as x-> +inf of y(x) equals 3 if y(0) > 0.

    Any help?
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  2. #2
    MHF Contributor chisigma's Avatar
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    A possible solution of the problem is a function y(x) with the following derivative y^{'} (x)...

    y^{'} < 0 with y>3 or y<0

     y^{'} =0 with  y=3 or y=0

    y^{'} >0 with 0<y<3

    A DE the solution of which has these properties is, among others, the following ...

    y^{'} = 3 y - y^{2}, y(0)=y_{0}>0

    ... as you can easily verify...

    Kind regards

    \chi \sigma
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