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Linear functions

  1. Mar 5, 2006 #1
    having the following equation, where F(x) is a function, and c is a constant independent of x, i am to find the non linear terms of the equation:

    [tex]cF(x)\frac{dF(x)}{dx}+\frac{d^2F(x)}{dx^2}+ic^2 \left (\frac{1}{F(x)}+F(x) \right) =0[/tex]

    i'm not sure where to start or start. could someone guide me in the right direction?
  2. jcsd
  3. Mar 5, 2006 #2


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    What do you have for a definiton of linear?
  4. Mar 5, 2006 #3
    functions where x is raised to the first power? is this the definition that i should use?
    Last edited: Mar 5, 2006
  5. Mar 5, 2006 #4
    I think what Integral meant was "What is the definition of a linear ordinary differential equation?"

  6. Mar 5, 2006 #5


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    Or, to put it another way, before you can decide which terms are non-linear, you have to know what "non-linear" terms look like! If you understand what "non-linear" and "linear" terms are you should be able to look at the equation and write down the answer without any computation.
  7. Mar 5, 2006 #6
    linear ordinary differential equation should be in the form a(x)y''+b(x)y'+c(x)y=d(x)
  8. Mar 5, 2006 #7
    So calling y=F(x), what terms in your original equation don't look linear?

  9. Mar 5, 2006 #8
    my equation would then become:


    the non linear part is then: [tex] \frac{ic^2}{F(x)}[/tex]

  10. Mar 6, 2006 #9


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    No. There is another non-linear term in there. Remember it is not just y that counts but derivatives of y also.
  11. Mar 6, 2006 #10
    [tex]y''+cyy'+\frac{ic^2 }{y}+ic^2y =0[/tex]

    so do you mean cyy' is a non-linear term too along with [tex]\frac{ic^2 }{y}[/tex]?
  12. Mar 6, 2006 #11

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