# Math Help - what is this?

1. ## 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?

2. i think you should try dividing by x and then y=zx

3. I have tried many methods but don't know what to do with 'ln' to separate y and x

4. Originally Posted by hekt
I have tried many methods but don't know what to do with 'ln' to separate y and x
$\ln \left (\frac{x}{y} \right) = \ln(x) - \ln(y)$

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...

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

$\chi$ $\sigma$