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Notation question

  1. Feb 1, 2007 #1
    Hi, Just a question on notation. What does [tex]F(\frac{y}{x}) [/tex] mean?

    It is in the context of..."the differential equation [tex] y' = F(\frac{y}{x}) [/tex] can be solved dadadadada........"

  2. jcsd
  3. Feb 1, 2007 #2
    It just means the right-hand side is a function of y/x. This could be a constant function, like F(y/x)=0, which would be trivial and silly, or something like F(y/x) = (y/x)^2 + (1/2)(y/x). Basically, if you can rearrange the right-hand side of the equation to explicitly be a function of y/x, whatever follows in your text will hold.
    For example, if you have the equation y' = x + 2, there is no way to write the right-hand side as a function of y/x. Writing it as y' = x*(y/x)*(y/x)^(-1) + 2 still includes x independently, so whatever follows that sentence in your book will not work for this type of equation.
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