How to prove invariance of I in this system?

[rg2004]

Homework Statement

Show that I = log(u)-u+2log(v)-v is an invariant of the following system
$\dot{u}=u(v-2)$

$\dot{v}=v(1-u)$

Homework Equations

The Attempt at a Solution

The question was given on a homework assignment, but I have very little idea what it is asking for and even less of an idea of how to solve it.

 

[tiny-tim]

hi rg2004!

Show that I = log(u)-u+2log(v)-v is an invariant of the following system …

it just means that I-dot is zero