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Find the solution of this differential equation

  1. Jun 15, 2008 #1
    1. The problem statement, all variables and given/known data

    if
    [tex]f \left( x,y \right) =xy*g \left( 7\,{x}^{2}-9\,{y}^{2} \right)[/tex]
    then the differential equation [tex]9y\frac{{\partial f}}{{\partial x}} + 7x\frac{{\partial f}}{{\partial y}} = ?[/tex] is equal to?

    2. Relevant equations
    --


    3. The attempt at a solution
    i triedto do a partial derivatives wich doesnt really seem to work
    if you can just give me a direction in which to go to
    thanks
     
  2. jcsd
  3. Jun 15, 2008 #2

    tiny-tim

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    Hi supercali! :smile:

    I don't see what doesn't really seem to work … which might be because you haven't told us! :rolleyes:

    (you do know they don't want you to solve the equation, only to write it out?)
     
  4. Jun 15, 2008 #3
    i dont think i really understand what it is i need to do
     
  5. Jun 15, 2008 #4

    tiny-tim

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    Just write out ∂f/∂x, and multiply it by 9y … :smile:

    (they haven't told you what g' is, so just leave it as g')

    (you do understand that g is an ordinary function, don't you?)
     
  6. Jun 15, 2008 #5
    no thats not what they want me to do
    they want me to form a differential equation the answer suppose to be with f ,x and y
    but i just dont think i understand how to do so
     
  7. Jun 15, 2008 #6
    Find
    1. df/dx
    df/dy

    g(mess) is a function, so use chain rule for it

    2. Substitute df/dx and df/dy in your target equation

    I think you misunderstood tiny-tim. You don't write out but do substitution.

    You don't need anything else (I can say for sure :) )
     
  8. Jun 16, 2008 #7

    tiny-tim

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    Hi supercali! :smile:

    No … they want you to form a differential equation with g x and y.

    f should disappear :smile:
     
  9. Jun 16, 2008 #8
    now i have the question infront of me the say there that they want the answer in terms of y x and f not g
     
  10. Jun 16, 2008 #9

    tiny-tim

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    no wonder you're confused …

    once you've done ∂/∂x to f, the f has gone!

    all that's left is x and y and g and g'

    Anyway, as rootX says, just work your way through it! :smile:
     
  11. Jun 16, 2008 #10
    solution:derive f
    [tex]9\,y \left( yg \left( 7\,{x}^{2}-9\,{y}^{2} \right) +14\,{x}^{2}y
    \mbox {D} \left( g \right) \left( 7\,{x}^{2}-9\,{y}^{2} \right)
    \right) +7\,x \left( xg \left( 7\,{x}^{2}-9\,{y}^{2} \right) -18\,x{y
    }^{2}\mbox {D} \left( g \right) \left( 7\,{x}^{2}-9\,{y}^{2} \right)
    \right) [/tex]
    gives:
    [tex]9\,{y}^{2}g \left( 7\,{x}^{2}-9\,{y}^{2} \right) +7\,{x}^{2}g \left( 7
    \,{x}^{2}-9\,{y}^{2} \right)[/tex]
    since [tex]f= xyg \left( 7\,{x}^{2}-9\,{y}^{2} \right)[/tex]
    we can get an expretion for y*g and x*g thus the final answer is
    [tex]9\,{\frac {yf}{x}}+7\,{\frac {xf}{y}} [/tex]

    thanks for all the help
     
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