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Trouble with Initial Value Condition Questions

  1. Jul 28, 2012 #1
    I have been looking at an example of a initial value condition problem in my notes and don't really understand where the solution came from. Here is the question:

    Let z(x,y)= 2x+ g(xy) and add the initial value conditon, z= x on the line y=1. Find the general solution of the initial value problem.


    1. Replace z(x,y)=2x+g(xy) wih the condition to get x= 2x+g(x) for all x, so that g(x)= -x

    I understand everything so far but then the next step says "hence z(x,y)= 2x-xy is the general solution." Where does the -xy come from?

    Any help or advice would be much appreciated! Thank you
     
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  3. Jul 28, 2012 #2

    Simon Bridge

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    Can you find another relation that would fit the conditions?
     
  4. Jul 29, 2012 #3

    HallsofIvy

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    It's just a matter of the "functional notation" you have been using for years:

    If g(x)= -x then g(u)= -u, g(a)= -a, g(v)= -v, etc.

    In eactly the same way, g(xy)= -xy.
     
  5. Jul 30, 2012 #4
    OK I understand now, thank you
     
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