(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Given this ODE:

x' = x+y-xy^2

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

and a function: u(x,y) = x^2+y^2-2ln|xy-1|

prove that for each soloution ( x(t), y(t) ) of this system, such as: x(t)*y(t) != 1 (doesn't equal...) , there exists a constsnt C such as: u ( x(t), y(t) ) = C for every t in R.

2. Relevant equations

3. The attempt at a solution

It's very clear that we need to look at the deriative of u... If it will be 0, then we'll get what we need...But since I haven't got that much knowledge in 2 variables functions, I can't realy see what is the deriative of u, as well as how to solve this ODE...

So, I realy need your help in:

1. Solving the ODE.

2. What is the deriative of u(t)?

TNX a lot!

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# Homework Help: ODE question 2

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