Notation question for an ODE

  • #1
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Hi PF!

Suppost I had some differential equation, say $$y'(x) + axy(x) +7a =0$$ where ##y=f(x)## and ##a## is some parameter. How do you reference this differential equation with different ##a## values are plugged in? Would I say $$ F(x,y;a) \equiv y'(x) + axy(x) +7a =0$$ and then when referencing an ##a## value of ##12## simply say ##F(x,y;12)##?

Thanks
 

Answers and Replies

  • #2
Simon Bridge
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The LHS is a specific instance of ##F(x,y(x),y'(x))## if you want to characterize it by a key parameter, then you write ##F_a(x,y,y')## for discrete parameters, and ##F(x,y,y',a)=0## for continuous parameters. There is no functional difference between a parameter that is allowed to vary and any other kind of variable.

I don't think there is a universal notation though - define your own. i.e. if F is defined to be y'+axy+7a then F(a) is enough to specify the particular F you mean.
 
  • #3
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Thanks a ton! This is all I wanted!
 
  • #4
Simon Bridge
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I forgot one: in statistics there is a standard notation ... ##f(x|a,b)## signifies a general function of x with parameters a and b, which have to be specified.
The pipe character "|" reads "given" and you also see it in conditional probability statements.
 

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