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Finding a simple ODE

  1. May 18, 2007 #1
    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 [tex] y=Cx^k \\ [/tex], where C and k are constant.
    I really don't know how to start this off, I have [tex] \frac{X}{Y} \propto \frac{x}{y} \\ [/tex]. What is the next step? Do I express X in terms of x and Y in terms of y? Thanks for helping.
     
  2. jcsd
  3. May 18, 2007 #2

    Dick

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    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'.
     
  4. May 18, 2007 #3
    Does it say x'/y'=k*x/y, where x=x(t) e.t.c.
     
  5. May 18, 2007 #4

    Dick

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    Sure. Now can you solve that ODE?
     
  6. May 18, 2007 #5
    I think I can.
     
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