Finding a simple ODE

1. May 18, 2007

John O' Meara

A mixture of two liquids X and Y, is boiling. At any time t there is present in the mixture a quantity x of one and y of the other. The ratio of the amounts of X and Y passing off at any one time is proportional to the ratio of the quantities still in the liquid state. Prove that $$y=Cx^k \\$$, where C and k are constant.
I really don't know how to start this off, I have $$\frac{X}{Y} \propto \frac{x}{y} \\$$. What is the next step? Do I express X in terms of x and Y in terms of y? Thanks for helping.

2. May 18, 2007

Dick

Well, what is X/Y? X and Y are just labels. x and y are the quantities. Read the problem again and tell me what it says about the relation between x,y and x',y'.

3. May 18, 2007

John O' Meara

Does it say x'/y'=k*x/y, where x=x(t) e.t.c.

4. May 18, 2007

Dick

Sure. Now can you solve that ODE?

5. May 18, 2007

John O' Meara

I think I can.