Originally Posted by

**kyz1024** Very sorry, I've posted the question wrong. My problems remain though...

The actual question should have read:

$\displaystyle x'=x^2+a-y$

$\displaystyle y'=b(x-2y)/c$ (*)

The conserved quantity is:

$\displaystyle

bx^2/2-y(a+x^2)+y^2/2

$

Here's what I did with it though, maybe this will help...

If you ignore the 'c'.

Then you can do the following.

$\displaystyle x'=x^2+a-y $

so

$\displaystyle

x'-x^2-a+y=0

$

then multiply through by [tex] y' [\math] to get

$\displaystyle x'y'-x^2y'-ay'+yy'=0$

then substitute (ignoring c) $\displaystyle y'=x(b-2y) $ (*) to get

$\displaystyle

bxx'-2xx'y-x^2y'-ay'+yy'=0

$

Which you can integrate to get:

$\displaystyle

bx^2/2-ay-x^2y+y^2/2=constant

$

Which gives the result. Don't know how to do it with the c though.