Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Definitions regarding DE

  1. Apr 19, 2014 #1
    I'm not sure if this is particularly important, but so far through my studies I've only encountered DE with two related variables (e.g. ## \frac {dy}{dx} = 3x##).

    Now, given another function with an additional variable that is UNRELATED to the two other variables, can this still be considered a differential equation (e.g. ## \frac {dy}{dx} = 3x + z## where z is a random variable)? Does this not meet it's definition?

    If I'm not mistaken, all the variables have to be related and it is possible to have DE with infinite variables, as long as they are all related. Is my understanding wrong?
     
  2. jcsd
  3. Apr 19, 2014 #2

    Mark44

    Staff: Mentor

    I would say no. Your first equation above is an example of an ordinary differential equation, in which you typically have one variable as a function of another. The assumption is that y = f(x), for some unknown function of a single independent variable.

    Another type of differential equation is the partial differential equation, or PDE, in which you typically have a dependent variable that is a function of two or more independent variables, and the equation to be solved is some combination of partial derivatives of the unknown function.

    The notation dy/dx implies that y is a function of x alone. In a PDE you have partial derivatives of various orders, such as ##\frac{\partial f}{\partial x}## and ##\frac{\partial^2 f}{\partial x^2}## and so on.

    When you said that z is a random variable, you are probably unaware that "random variable" is a term widely used in statistics, with a specific meaning.
     
  4. Apr 20, 2014 #3

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    You can always solve the equation ##\frac{dy}{dx} = 3x + z## by treating ##z## as a constant (if it doesn't depend on ##x##). But we don't call ##z## a variable then, but rather a parameter.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Definitions regarding DE
  1. Is this DE linear? (Replies: 3)

  2. A doubt in the DE (Replies: 1)

  3. Constructing a DE (Replies: 3)

  4. DE question (Replies: 3)

Loading...