are differentials "dy" and "dx" considered variables?

Discussion in 'Math' started by PG1995, Nov 13, 2011.

  1. PG1995

    Thread Starter Active Member

    Apr 15, 2011
    753
    5
    Hi :)

    Please have a look on the attachment. You can find find my question there. Thank you for the help.

    Regards
    PG
     
  2. steveb

    Senior Member

    Jul 3, 2008
    2,433
    469
    Differentials can be variables, but in this context the x and y are the variables they are talking about that are separable.
     
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  3. thatoneguy

    AAC Fanatic!

    Feb 19, 2009
    6,357
    718
    Calculus and higher math run on expanding the concept of algebra.

    In algebra, a letter can denote any number, it has been found that a letter, say f(x) can represent any equation. The dx and dy components point to the 'working variables' of the function, which can be worked on using calculus formulas.

    An example is the forms of integration for a function F(x) if it fits certain models, the integration of such is known, so instead of x=sin(45) in algebra, f(x)=sin(x) dx in calculus, with x being the working variable.
     
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  4. panic mode

    Senior Member

    Oct 10, 2011
    1,321
    304
    as others have mentioned, x, y, t etc. are generally used as variables. and in this context they are still variables so you can use math to manipulate them.

    suppose you have
    dy/dt=k*y*t^2

    this is separable because you can separate y and t to get for example:

    dy/y=k*t^2*dt

    now it is easy to solve because all y are on one side and all t are on other.
    but you will not be lucky enough to only deal with separable variables.

    but suppose you have

    dy/dt +t*y= t^2

    as you can see there is a problem, can't just separate them...
     
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