What type of DE is this:

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

Should I solve it by substitution or any other way?

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- Apr 5th 2010, 07:39 AM #1

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- Apr 5th 2010, 11:17 AM #2

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- Apr 5th 2010, 11:30 AM #3

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- Apr 5th 2010, 01:46 PM #5
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...

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

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

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

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

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$