Basic Diff EQ question: finding a function with given properties

**qtpipi** · September 8th 2009, 10:41 PM

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?

**chisigma** · September 9th 2009, 04:09 AM

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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