isomorphic equations

Question

W. Ross Ashby states in his book "An Introduction to Cybernetics" that the system:

$\ x' = 1/2(x^2+y^2) + x*y + y$

$\ y' = 1/2(x^2+y^2) + x*y + x$

is isomorphic to the system:

$\ u' = -u$

$\ v' = v + v^2$

under the transformation:

$\ u = x - y$

$\ v = x + y$

can someone explain this properly?

Answer 1

Hint: Just compute $u'=x'-y'$ and $v'=x'+y'$.