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On solving PDE using separating the variable.

  1. May 5, 2013 #1
    hi..

    with refrenence to http://www.math.uah.edu/howell/MAPH/Archives/Old_Notes/PDEs/PDE1.pdf [Broken]
    page 7,
    “Observe” that the only way we can have
    formula of t only= formula of x only​
    is for both sides to be equal to a single constant.

    here I do understand that for these to being equal requires them to be constant, because changing either t or x would affect either side of the formula breaking the inequality, so to be equal they are supposed to be a constant. (please correct me if i go wrong anywhere..)
    Now what i am not sure about is that these two formulas can also be equal to each other for a specific value of x and t, is this anything to do with the constant that they will be equal to??

    It is said that the constant say k is arbitrary, suggesting these two sides are equal for more than one value of x and y... how is this said?

    (I gave the link so that i don't have to explain what i am asking, because i don't know the correct terms and that might turn confusing.. no copyright violation intended)
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. May 5, 2013 #2

    HallsofIvy

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    I'm not sure what you are asking here. If X(x)= T(t) for all x and t, then, yes, they must be equal to the same constant for all x and t, which, of course, includes any "specific value of x and t".

    (You mean "t" not "y", right?) What do you mean "for more than one value of x and t"?? You just said they were equal for all x and t. That surely includes more than one!

     
    Last edited by a moderator: May 6, 2017
  4. May 5, 2013 #3
    Okay i got it..
    If X(x) = T(t) for all x and t, and there is no relation or interdependence between x and t other than this, then X(x)= constant just as T(t). And this constant is constant for all values of x and t... Thanks for the quick help.
     
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