everyone! :-)
I've a ODE question with I can't solve. It's here: ${dy\over dx} = {{xy + 2y-x-2}\over {xy-3y+x-3}} $
I tried the following:
${dy\over dx} = {{xy + 2y-x-2}\over {xy-3y+x-3}}={(y-1)(x+2)\over (y+1)(x-3)} \Rightarrow \int {(y+1)dy\over(y-1)}=\int {(x+2)dx\over(x-3)}\ \ \ $ This has resulted in:
$\int {(y)dy\over(y-1)}+\int {dy\over(y-1)}=\int {(x)dx\over(x-2)}+2\int {dx\over(x-3)} \Rightarrow y+2ln|y-1|=x+5ln|x-3|$
I can not explain the function $y$. Can anyone help me showing how I do it? Thanks!